{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
       "            max-height:100000px;\n",
       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
       "            webkit-box-shadow:none !important;\n",
       "        }\n",
       "        </style>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement deviates far from the current track, like so (I'll only consider 1 dimension for simplicity):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BAOfOnQNQ11rg6OgIAAgJCYGLiwvCwsIAAIsXL8Zdd92FNWvW4P7778eePXsQGRmJQ4cOdfLdEREREZGUJGeVoFKtgZWpMfrYdRM7nA4l6uxG0dHR8PHxgY+PDwBg6dKl8PHxweuvvw4A+Omnn+Dj44MpU6YAAB555BH4+Pjgs88+054jPT0dWVlZ2tdjxozBjh07sGXLFgwdOhRbt27Fzp07MWrUqE68MyIiIiKSmriM+qlPu8PISJqLqNUTtSXBz88PgiA0u3/evHmYN2/eLc8RFRXVaNuMGTMwY8aMdkZHRERERHRTXHohAGmvj1BPcuskEBERERF1hNj0my0JUscigYiIiIjoNq6XViHtet30ocMkvIhaPRYJRERERES3EZ9RCADo52ABa3PDm9WotVgkEBERERHdhnY8gquNqHF0FhYJRERERES38feZjboCFglERERERLdQqxEQ34VmNgJYJBARERER3dL53BKUVdeim4kc/VWWYofTKVgkEBERERHdQv14BG9XG8glvohaPRYJRERERES3EKddH8FG3EA6EYsEIiIiIqJbuDmzUdcYtAywSCAiIiIialZRhRrnc0sBAMPYkkBERERERKduLKLWq4c57CyU4gbTiVgkEBERERE1o6stolaPRQIRERERUTO62iJq9VgkEBERERE1QaMRbrYkdKHxCACLBCIiIiKiJqVeL0NRhRpKYyMMdLQSO5xOxSKBiIiIiKgJ9a0IQ3taw8S4a31s7lp3S0RERETUQjcXUeta4xEAFglERERERE3qqjMbASwSiIiIiIgaKauqQXJ2MQC2JBAREREREYDTV4qgEQAna1M4WpuKHU6nY5FARERERPQP9esjDO+CrQgAiwQiIiIioka66voI9VgkEBERERH9jSB03UXU6olaJBw8eBDBwcFwdnaGTCbD7t27G+wXBAGhoaFwdnaGmZkZ/Pz8kJCQcNvzrl+/HgMGDICZmRlcXV3xwgsvoLKysoPugoiIiIik5EpBBfJKq6CQyzDI2VrscEQhapFQVlYGb29vbNiwocn9a9euxbp167BhwwacPHkSjo6OCAgIQElJSbPn/Oabb/Dqq6/ijTfeQFJSEjZv3oydO3di2bJlHXUbRERERCQhsTfWR/BytoapQi5yNOIwFvPiQUFBCAoKanKfIAhYv349li9fjunTpwMAtm3bBpVKhe3bt2PhwoVNHnf06FGMHTsWs2fPBgD07t0bs2bNwokTJzrmJoiIiIhIUrry+gj19HZMQmpqKrKzsxEYGKjdplQqMWHCBBw5cqTZ48aNG4eYmBhtUXDp0iXs3bsXU6ZM6fCYiYiIiMjwxWUUAui64xEAkVsSbiU7OxsAoFKpGmxXqVRIS0tr9rhHHnkE165dw7hx4yAIAmpqavD000/j1VdfbfaYqqoqVFVVaV8XF9ctnKFWq6FWq9tzG21Sf00xrk26xVxKC/MpHcyldDCX0qEvuaxS1yIxswgAMMTZQvR4dK2l96O3RUI9mUzW4LUgCI22/V1UVBTefvttfPrppxg1ahQuXLiAxYsXw8nJCStWrGjymLCwMKxcubLR9vDwcJibm7fvBtohIiJCtGuTbjGX0sJ8SgdzKR3MpXSIncvUEkBdawwLhYDTR6JwpvmPnQapvLy8Re/T2yLB0dERQF2LgpOTk3Z7bm5uo9aFv1uxYgXmzJmDBQsWAACGDBmCsrIy/Otf/8Ly5cthZNS4h9WyZcuwdOlS7evi4mK4uroiMDAQVlZWurqlFlOr1YiIiEBAQAAUCkWnX590h7mUFuZTOphL6WAupUNfcvnF4cvA2RTc2dcBU6b4iBZHR6nvMXM7elskuLu7w9HREREREfDxqUtQdXU1Dhw4gDVr1jR7XHl5eaNCQC6XQxAECILQ5DFKpRJKpbLRdoVCIeoPqdjXJ91hLqWF+ZQO5lI6mEvpEDuXp6/WzaI5vLetJH+mWnpPohYJpaWluHDhgvZ1amoq4uPjYWtrCzc3NyxZsgSrV6+Gh4cHPDw8sHr1apibm2tnLgKAkJAQuLi4ICwsDAAQHByMdevWwcfHR9vdaMWKFZg6dSrk8q45hRURERERtUzcjelPfVy7ixyJuEQtEqKjozFx4kTt6/ouP3PnzsXWrVvx8ssvo6KiAs888wwKCgowatQohIeHw9LSUntMenp6g5aD1157DTKZDK+99hquXr0Ke3t7BAcH4+233+68GyMiIiIig5NdVInMokoYyYChPbvmImr1RC0S/Pz8mu0CBNQNWg4NDUVoaGiz74mKimrw2tjYGG+88QbeeOMNHUVJRERERF1BfSvCQEcrdFPqba/8TqG36yQQEREREXUmro9wE4sEIiIiIiL8bTyCW9cejwCwSCAiIiIiQnWNBqev1C2ixpYEFglEREREREjOLkZVjQbWZgq49+gmdjiiY5FARERERF1eXHohgLpWBCMjiS2z3AYsEoiIiIioy+P6CA21aW6nsrIyvPPOO9i/fz9yc3Oh0Wga7L906ZJOgiMiIiIi6gyc2aihNhUJCxYswIEDBzBnzhw4OTlBJmOTDBEREREZprzSKqRdLwcAeLvaiBuMnmhTkbBv3z78+uuvGDt2rK7jISIiIiLqVPE3xiP0c7CAtZlC3GD0RJvGJHTv3h22tra6joWIiIiIqNPFZdSNRxjOrkZabSoS3nrrLbz++usoLy/XdTxERERERJ3q5sxGHLRcr03djd5//31cvHgRKpUKvXv3hkLRsFkmNjZWJ8EREREREXWkWo2AUxy03EibioRp06bpOAwiIiIios6XklOCsupaWCiN4eFgKXY4eqNNRcIbb7yh6ziIiIiIiDpdfVcjb1dryLmImlabioR6MTExSEpKgkwmg5eXF3x8fHQVFxERERFRh+Miak1rU5GQm5uLRx55BFFRUbCxsYEgCCgqKsLEiROxY8cO2Nvb6zpOIiIiIiKd4yJqTWvT7EbPP/88iouLkZCQgPz8fBQUFODs2bMoLi7GokWLdB0jEREREZHOFZWrcSG3FAAwjIuoNdCmloTffvsNkZGR8PT01G7z8vLCJ598gsDAQJ0FR0RERETUUeKvFAIAevUwRw8LpbjB6Jk2tSRoNJpG054CgEKhgEajaXdQREREREQdrX48wnCuj9BIm4qEu+++G4sXL0ZmZqZ229WrV/HCCy9g0qRJOguOiIiIiKij3FxEzUbUOPRRm4qEDRs2oKSkBL1790bfvn3Rr18/uLu7o6SkBB9//LGuYyQiIiIi0imNRkB8/aBlzmzUSJvGJLi6uiI2NhYRERFITk6GIAjw8vKCv7+/ruMjIiIiItK5S3llKKpQw1RhhIFOXETtn9q1TkJAQAACAgJ0FQsRERERUaeoH48w1MUGCnmbOtdIWouLhI8++gj/+te/YGpqio8++uiW7+U0qERERESkz7g+wq21uEj44IMP8Oijj8LU1BQffPBBs++TyWQtLhIOHjyId999FzExMcjKysKuXbswbdo07X5BELBy5Up8/vnnKCgowKhRo/DJJ59g0KBBtzxvYWEhli9fjh9//BEFBQVwd3fH+++/j3vvvbdFcRERERGRtHHQ8q21uEhITU1t8v/bo6ysDN7e3pg/fz4efPDBRvvXrl2LdevWYevWrejfvz9WrVqFgIAAnDt3DpaWTfcdq66uRkBAABwcHPD999+jZ8+eyMjIaPb9RERERNS1lFXV4Fx2MQDAh9OfNqlNYxLefPNNvPTSSzA3N2+wvaKiAu+++y5ef/31Fp0nKCgIQUFBTe4TBAHr16/H8uXLMX36dADAtm3boFKpsH37dixcuLDJ47744gvk5+fjyJEj2rUcevXq1dJbIyIiIiKJO3WlEBoBcLY2hcrKVOxw9FKbRmmsXLkSpaWljbaXl5dj5cqV7Q4KqGutyM7ObrCCs1KpxIQJE3DkyJFmj/vpp58wevRoPPvss1CpVBg8eDBWr16N2tpancRFRERERIZN29WoF1sRmtOmlgRBECCTyRptP3XqFGxtbdsdFABkZ2cDAFQqVYPtKpUKaWlpzR536dIl/PHHH3j00Uexd+9enD9/Hs8++yxqamqabeGoqqpCVVWV9nVxcV3zk1qthlqtbu+ttFr9NcW4NukWcyktzKd0MJfSwVxKR2fmMjYtHwDg7WLV5X52Wnq/rSoSunfvDplMBplMhv79+zcoFGpra1FaWoqnnnqqdZHexj+LkeYKlHoajQYODg74/PPPIZfLMWLECGRmZt6yG1RYWFiTLSDh4eGNulR1poiICNGuTbrFXEoL8ykdzKV0MJfS0dG5FATg+EU5ABnKMxKwd29Ch15P35SXl7fofa0qEtavXw9BEPD4449j5cqVsLa21u4zMTFB7969MXr06NZF2gxHR0cAdS0KTk5O2u25ubmNWhf+zsnJCQqFAnK5XLvN09MT2dnZqK6uhomJSaNjli1bhqVLl2pfFxcXw9XVFYGBgbCystLF7bSKWq1GREQEAgICtOMqyDAxl9LCfEoHcykdzKV0dFYu0/PLUXrsEBRyGRZMnwylQn77gySkvsfM7bSqSJg7dy4AwN3dHWPGjOnQBLq7u8PR0RERERHw8fEBUDdz0YEDB7BmzZpmjxs7diy2b98OjUYDI6O6IRcpKSlwcnJqskAA6sY6KJXKRtsVCoWoDxyxr0+6w1xKC/MpHcyldDCX0tHRuTybVTeu1svZGhbmXW/Qckv/bVs8cPnvVYePjw8qKipQXFzc5H8tVVpaivj4eMTHxwOoG6wcHx+P9PR0yGQyLFmyBKtXr8auXbtw9uxZzJs3D+bm5pg9e7b2HCEhIVi2bJn29dNPP43r169j8eLFSElJwa+//orVq1fj2WefbXFcRERERCRN9YOWh3N9hFtqcUtC9+7dkZWVBQcHB9jY2DQ5LqB+vEBLZxKKjo7GxIkTta/ru/zMnTsXW7duxcsvv4yKigo888wz2sXUwsPDG6x5kJ6erm0xAABXV1eEh4fjhRdewNChQ+Hi4oLFixfjlVdeaemtEhEREZFExaUXAOD6CLfT4iLhjz/+0M5c9Oeff+rk4n5+fhAEodn9MpkMoaGhCA0NbfY9UVFRjbaNHj0ax44d00GERERERCQVlepaJGTeWETN1UbcYPRci4uECRMmNPn/RERERESG4OzVItRoBNhZKNGzu5nY4ei1Ni2m9ttvv+HQoUPa15988gmGDRuG2bNno6CgQGfBERERERHpyt/HI9xqSn1qY5Hw73//WztA+cyZM1i6dCnuvfdeXLp0qcFUokRERERE+iIug+MRWqpNKy6npqbCy8sLAPDDDz8gODgYq1evRmxsLO69916dBkhEREREpAv1LQk+nNnottrUkmBiYqJdrS0yMhKBgYEAAFtb21ZNgUpERERE1BmyiiqQVVQJIxkwtKf17Q/o4trUkjBu3DgsXboUY8eOxYkTJ7Bz504AdYuW9ezZU6cBEhERERG1V30rwkBHK5ibtOkjcJfSppaEDRs2wNjYGN9//z02btwIFxcXAMC+fftwzz336DRAIiIiIqL2ql8fYXgvG3EDMRBtKqPc3Nzwyy+/NNr+wQcftDsgIiIiIiJd045HcOWg5ZZoc1tLbW0tdu/ejaSkJMhkMnh6euL++++HXC7XZXxERERERO1SXaPBmatFADhouaXaVCRcuHAB9957L65evYoBAwZAEASkpKTA1dUVv/76K/r27avrOImIiIiI2iQpqxhVNRpYmyngbtdN7HAMQpvGJCxatAh9+/ZFRkYGYmNjERcXh/T0dLi7u2PRokW6jpGIiIiIqM3qxyP4cBG1FmtTS8KBAwdw7Ngx2Nraarf16NED77zzDsaOHauz4IiIiIiI2isuoxAAMJyLqLVYm1oSlEolSkpKGm0vLS2FiYlJu4MiIiIiItIVLqLWem0qEu677z7861//wvHjxyEIAgRBwLFjx/DUU09h6tSpuo6RiIiIiKhN8kqrkJ5fDpkM8Ha1ETscg9GmIuGjjz5C3759MXr0aJiamsLU1BRjxoxBv3798OGHH+o6RiIiIiKiNqlvRehnbwErU4W4wRiQNo1JsLGxwZ49e3DhwgUkJiYCALy8vNCvXz+dBkdERERE1B7aRdQ4HqFV2rxOwubNm/HBBx/g/PnzAAAPDw8sWbIECxYs0FlwRERERETtwfEIbdOmImHFihX44IMP8Pzzz2P06NEAgKNHj+KFF17A5cuXsWrVKp0GSURERETUWrUaAaeuFAIAfNiS0CptKhI2btyITZs2YdasWdptU6dOxdChQ/H888+zSCAiIiIi0Z3LLkF5dS0slMbo52AhdjgGpU0Dl2tra+Hr69to+4gRI1BTU9PuoIiIiIiI2isuo248grerNeRGXEStNdpUJDz22GPYuHFjo+2ff/45Hn300XYHRURERETUXvXjEThoufXaNXA5PDwcd955JwDg2LFjyMjIQEhICJYuXap937p169ofJRERERFRK9XPbMRBy63XpiLh7NmzGD58OADg4sWLAAB7e3vY29vj7Nmz2vfJZGzWISIiIqLOV1SuxsVrZQCAYa5sSWitNhUJf/75p67jICIiIiLSmfrxCL17mMO2m4nI0RieNo1J0JWDBw8iODgYzs7OkMlk2L17d4P9giAgNDQUzs7OMDMzg5+fHxISElp8/h07dkAmk2HatGm6DZyIiIiI9BrHI7SPqEVCWVkZvL29sWHDhib3r127FuvWrcOGDRtw8uRJODo6IiAgACUlJbc9d1paGl566SWMHz9e12ETERERkZ6LyygEwPEIbdXmgcu6EBQUhKCgoCb3CYKA9evXY/ny5Zg+fToAYNu2bVCpVNi+fTsWLlzY7Hlra2vx6KOPYuXKlfjrr79QWFjYEeETERERkR7SaATEawctsyWhLURtSbiV1NRUZGdnIzAwULtNqVRiwoQJOHLkyC2PffPNN2Fvb48nnniio8MkIiIiIj1zKa8MxZU1MFUYYYCjpdjhGCRRWxJuJTs7GwCgUqkabFepVEhLS2v2uMOHD2Pz5s2Ij49v8bWqqqpQVVWlfV1cXAwAUKvVUKvVrYhaN+qvKca1SbeYS2lhPqWDuZQO5lI6dJnLk6l5AIDBzlaAphZqTW27zykVLf331dsiod4/p1EVBKHZqVVLSkrw2GOPYdOmTbCzs2vxNcLCwrBy5cpG28PDw2Fubt66gHUoIiJCtGuTbjGX0sJ8SgdzKR3MpXToIpc/XzQCYARrdT727t3b/qAkpLy8vEXv09siwdHREUBdi4KTk5N2e25ubqPWhXoXL17E5cuXERwcrN2m0WgAAMbGxjh37hz69u3b6Lhly5Y1WACuuLgYrq6uCAwMhJWVlU7upzXUajUiIiIQEBAAhULR6dcn3WEupYX5lA7mUjqYS+nQZS43bjgCoBTTJ/gg0Kvpz41dVX2PmdvR2yLB3d0djo6OiIiIgI+PDwCguroaBw4cwJo1a5o8ZuDAgThz5kyDba+99hpKSkrw4YcfwtXVtcnjlEollEplo+0KhULUB47Y1yfdYS6lhfmUDuZSOphL6WhvLkurapCSWwoA8HW348/FP7T030PUIqG0tBQXLlzQvk5NTUV8fDxsbW3h5uaGJUuWYPXq1fDw8ICHhwdWr14Nc3NzzJ49W3tMSEgIXFxcEBYWBlNTUwwePLjBNWxsbACg0XYiIiIikp7TGYXQCICLjRlUVqZih2OwRC0SoqOjMXHiRO3r+i4/c+fOxdatW/Hyyy+joqICzzzzDAoKCjBq1CiEh4fD0vLmKPX09HQYGentJE1ERERE1Inq10cYxvUR2kXUIsHPzw+CIDS7XyaTITQ0FKGhoc2+Jyoq6pbX2Lp1a9uCIyIiIiKDE3djfQSutNw+/AqeiIiIiCRBEATEpRcC4ErL7cUigYiIiIgkISO/AtfLqmEiN8Ig586foVJKWCQQERERkSTE3uhq5OVsBaWxXORoDBuLBCIiIiKSBI5H0B0WCUREREQkCfUzG3E8QvuxSCAiIiIig1eprkViZt1qwiwS2o9FAhEREREZvLNXi1CjEWBvqYSLjZnY4Rg8FglEREREZPDqBy37uNpAJpOJHI3hY5FARERERAavfn2E4b04aFkXWCQQERERkcHTLqLmaiNqHFJhLHYAREQkvqJyNaJSchGZlItKdS2e9uvLKQSJyGBkFVUgu7gSciMZhvS0FjscSWCRQETURaVdL0NEYg72J+XixOV81GoE7b6IxBw8MtIVr9wzEN27mYgYJRHR7cWmFQIABjpawtyEH291gf+KRERdRK1GQHxGASKTchGZmIPzuaUN9vdXWcDfU4Wc4ir8EHsFO05m4PeEbLxyz0DM9HWFkREHAhKRfuIiarrHIoGISMLKq2vw1/k8RCbm4I/kXFwvq9bukxvJMMrdFv6eKvh7quDWw1y775E7XLFi91kkZ5fg1R/PYGd0BlZNG4xBzmzGJyL9w0XUdI9FAhGRxGQXVWJ/cg4iE3Nw+OJ1VNdotPssTY0xcYADJnk6wK+/A6zNFU2eY2RvW/z8/DhsO3IZH0SkIC69EMEfH0LI6N5YGtgfVqZNH0dE1NmqazQ4c7UIAODDlgSdYZFARGTgBEFAQmYx9iflIjIpR/vHsp6rrRkCPB3h7+mAke62UMhbNrGdQm6EBeP74L6hzlj1ayJ+OZ2FrUcu45fTWXhtiifuH+bMuciJSHRJWcWortHAxlyB3n9rEaX2YZFARGSAqmpqcexSPiITc7A/KQeZRZXafTJZ3RSA/l513Yg8HCza9WHe0doUG2YPxyMj8/D6nrO4lFeGJTvjseNkOt66fzA8VJa6uCUiojbhImodg0UCEZGByC+rxp/Jda0FB1Ouoay6VrvPTCHHeA87+HuqMHGgA+wtlTq//jgPO+xbMh7//SsVH+0/j2OX8hH04V94Yrw7Ft3tgW5K/kkhos6nXUSNXY10ik90IiI9dvFaKSITcxCZlIOYtAL8bZZSOFgqb7QWOGBMXzuYKuQdHo/SWI5nJ/bDVG9nrPw5AZFJufi/A5fwc3wmXg/2wuRBjvwmj4g6VVzGjZYEFgk6xSKBiEiP1NRqEJNWgMikHEQm5SI1r6zBfi8nK/h7OsDfS4XBztaiTUvqamuO/84dicjEHIT+nIArBRV46utY+A2wx8qpg9CrRzdR4iKiruVaSRUy8isgkwFDXTn7mi6xSCAiEllJpRoHU/IQmZSDP8/lorBcrd2nkMswuq8d/D0dMMlTBRcbMxEjbczfS4Wx/ezwyZ8X8H8HLyLq3DUEfHAQz/j1xVMT+nZK6wYRdV3xN6Y+9XCw4KxrOsYigYhIBFcKyrWzER27dB3q2pv9iGzMFbh7oAP8PVUY72EHSz3/w2dmIsdLkwfggeEueGNPAg5dyMP6yPPYFXcVoVMHYeIAB7FDJCKJujlomV2NdI1FAhFRJ9BoBJy5WoTIpBxEJOYgObukwf4+9t20i5oNd7OBcQunKdUnfe0t8NUTd+DXM1l465dEpF0vx/wtJ3HPIEe8HuwFZz1rBSEiw6ddabmXjbiBSBCLBCKiDlKprsXhC3XdiPYn5SK3pEq7z0gG+Pa21XYj6mtvIWKkuiOTyXDfUGf4DXDA+ogUbDlyGb8lZONAyjUs9vfA42PdYWJseAUQEemfmloNTl/hImodRdQn9cGDBxEcHAxn57oFeXbv3t1gvyAICA0NhbOzM8zMzODn54eEhIRbnnPTpk0YP348unfvju7du8Pf3x8nTpzowLsgIrrpWkkVdp5Mx5NfRmPYm+F4Yls0vj2RgdySKnQzkePeIY5YN9MbMa8F4LuFo/Gvu/pKpkD4OwulMV67zwu/LhqHkb27o0Jdi3f2JePej/7C0YvXxQ6PiCQgJacU5dW1sFQao58En6NiE7UloaysDN7e3pg/fz4efPDBRvvXrl2LdevWYevWrejfvz9WrVqFgIAAnDt3DpaWTS/eExUVhVmzZmHMmDEwNTXF2rVrERgYiISEBLi4uHT0LRFRFyMIAlJySm/MRpSD+IxCCH+bptTZ2lS7qNmoPrZQGnetgbwDHa3w3cLR+CH2KsL2JuFCbilmbTqGacOc8Z8pnnCwNBU7RCIyUPXjEbxdbUSb6U3KRC0SgoKCEBQU1OQ+QRCwfv16LF++HNOnTwcAbNu2DSqVCtu3b8fChQubPO6bb75p8HrTpk34/vvvsX//foSEhOj2BoioS1LXanAiLQ8RiTnYn5yDjPyKBvuH9rTWji/wdLLs8usGyGQyzBjREwGeKrwbnoxvjqdjd3wm9ifl4sXA/njszl4GOQaDiMR1cxE1G1HjkCq9HZOQmpqK7OxsBAYGarcplUpMmDABR44cabZI+Kfy8nKo1WrY2tp2VKjUBiWVapy5UgQft+4wM+la36ySYSoqV2N/Uha+TjHCa3FRKKms0e5TGhthbL+61Y4neTpAZcVvx5tiba7AqmlD8NAIV6zYcxanrxQh9OdEfBd9BaseGMzVUqlNcoorcaXs9u8j6eEiah1Lb4uE7OxsAIBKpWqwXaVSIS0trcXnefXVV+Hi4gJ/f/9m31NVVYWqqpsDCouLiwEAarUaarW6ucM6TP01xbh2R8osrMAf565hf/I1HE/Nh7pWwHA3G3w53xdKiQ5klGouu4q0/HL8kXwNfyTn4mRaIWo1AuqGctWgRzcTTBxgj0kD7TGmry3MTW4+TpnvW/Ny7IbvnrwDO6Ov4P2I80jMKsb0T49g5ggXvBToge7mJh0eA383pSE6rQALv45DcaUxTqnj8NoUTzhZs0g3VK35vSwsV+PStbrqcJBTN/4ut0JL/630tkio989mekEQWtx0v3btWnz77beIioqCqWnzD42wsDCsXLmy0fbw8HCYm5u3LmAdioiIEO3auqARgIwyICHfCGcLZLha3jBvMgiITS/EE5+GY1ZfDaTcI8PQc9lVaAQgrRQ4e+NnNrui4Q+lo5mAwbYChnTXwM2iBkayNFSnpiEqVaSADZwNgJcHAz+lGeHENSN8F3MVv566gmA3DUY5COiMLsb83TRcZ/Jl2JZiBLVQ94MSnnQNUedycU9PDfycBLAHm+Fqye9lUoEMgBz2pgKORkV2fFASUl5e3qL36W2R4OjoCKCuRcHJyUm7PTc3t1HrQlPee+89rF69GpGRkRg6dOgt37ts2TIsXbpU+7q4uBiurq4IDAyElZVVG++g7dRqNSIiIhAQEACFQr8XUfqnSnUtjl7Kx/7ka/jz3LVGUz4Od7PB3QPtMWmAA64WVWDBl7E4fs0Ik3w9MX9MLxEj7xiGnMuuory6Bocv5GP/uVz8ee4a8stufsNibCTDyN7dcfdAe9w9wB5OlgrmswM8jLpvhEN/TsK5nFLsuCRHstoaK4M94eXUMc9g/m4atu9jr2LL8UTUCgL8PHpguDIHUUU9EJtRhJ/S5Uis6IbQYE+McmdXY0PSmt/L8/svAMmXMHaAM+69d0gnRSgN9T1mbkdviwR3d3c4OjoiIiICPj4+AIDq6mocOHAAa9asueWx7777LlatWoXff/8dvr6+t72WUqmEUqlstF2hUIj6x0Ps67fUtZIq/Jmci4ikHBw6n4cKda12XzcTOe7qbw9/TxUmDnSAbbeb3QgGONtg+RQvvPVLIt757RwGOFljQn97MW6hwxlKLruK7KJK7E/OQWRiDg5fvI7qGo12n6WpMSYOcIC/lwoT+tvD2uxm3uqbaJlP3RvdzwG/LLLDtiOX8UFECuIzivDAxmMIGd0bSwP7w6qDVp1mLg2LIAj47MAlrPktGQAwY0RPvBU8EOG//4YdM+/AT2dy62bRulaGx76IxgM+Llh270DOomVgWvJ7eepq3QfdEe49+DvcSi399xK1SCgtLcWFCxe0r1NTUxEfHw9bW1u4ublhyZIlWL16NTw8PODh4YHVq1fD3Nwcs2fP1h4TEhICFxcXhIWFAajrYrRixQps374dvXv31o5tsLCwgIUF59DVBUEQcD63FBGJzU/5OMlTBX8vFe68zZSPj4/tjXPZxfgu+gqe2x6L3c+OleSc8SQuQRCQmFWMyMRcRCbl4MzVogb7XW3NEODpCH9PB4x0t4WC/RREoZAbYcH4PrhvqDNW/ZqIX05nYeuRy/j1TBaW3+uJ+4c5d/mZoroyjUbA23uTsPlQXf++hRP64NV7BqKmpm4SgaZm0doVdxWRiTl4afIAPHZnL8g5TaYkaDQC4jMKAQA+rjaixiJlohYJ0dHRmDhxovZ1fZefuXPnYuvWrXj55ZdRUVGBZ555BgUFBRg1ahTCw8MbrJGQnp4OI6Obf9A//fRTVFdXY8aMGQ2u9cYbbyA0NLRjb0jC1LUanEzNR8SNueD/OeXjEJcbUz56OcDLyarFf8hlMhnemjYYF6+VISatAE9ui8auZ8bC2pzfClD7VNXU4tilfEQm5mB/Ug4yiyq1+2Syuj8s9esXeDhY8MOnHnG0NsWG2cPxyMg8vL7nLC7llWHJznjsOJmOt+4fDA9V0+vkkHSpazV4+fvT2BV3FQDw2hRPLBjfp8n3NjWL1hs/JeC76AysmjaYM+FIwKW8UpRU1sBUYYSBjnwedBRRiwQ/Pz8If/8K+h9kMhlCQ0Nv+eE+KiqqwevLly/rJjhCUYUaUedyEZmUi6hzuQ2mfDQxNsLYvj3g76XCpIEqOLZjNgmlsRyfPTYC9284hEt5ZXju21hsmTeS86ZTq+WXVePP5LrWgoMp11BWfbPrm5lCjvEedtqub/aWjbsYkn4Z52GHfUvG479/peKj/edx7FI+gj78CwvG98GiSf0azChF0lVeXYOnv47FgZRrMDaS4d2HhuIBn563Pc7b1Qa7nhmL7SfS8e5vyUjILMb0jUfwyEhXvDx5ILp36/hZtKhjxKYVAgCG9rThZ4UOxCcsNZB2vQyRSbmITMzBycv5qNHcLOJ6dDPB3QPr+mqP62eHbkrd/fjYWyqxaa4vZmw8ir/O52H13mS8Huyls/OTdF28VorIG13fYtIK8LcfWThYKjHJU4UALweM6WsHUwXX5DA0SmM5np3YD1O9nbHy5wREJuXiswMX8VP8Vbwe7IXJgxzZCiRhBWXVmL/1JOIzCmGmkOPTx4Zj4gCHFh8vN5Jhzp29EDTYEWF7k/FD7BV8eyIDv53NxqtBA/HQCFeu1GuAbq6PYCNuIBLHIqGLq73Rry8yqW4Q5/nc0gb7PRwstF0yhrnadGh/zkHO1lg30xtPfxOLLw6nYqCjJWaOdO2w65FhqqnVICatAJFJOdiflItLeQ1XUfJysoK/Z10xO9jZmh8AJMLV1hz/nTsSEYk5CP0pAVcLK/DU17HwG2CPlVMHoVePbmKHSDqWWViBkC9O4EJuKWzMFfhi3sg2L7hnZ6HE+zO98fBIV6zYfRbnckrwyg9nsPNkBt6aNhiDnK11HD11pJsrLbPrWEdikdAFlVfX4K/zeYhMzMGf53KRV1qt3Sc3kuGO3rY3CgOHTv/DGzTECUv8PbA+8jyW7z6DPvbd4NubU9h1dSWVahxMyUNkUt3PbGH5zWlKFXIZ7uzTAwFeKkzyVMHFxkzESKmjBdxoyfzkzwv4v4MXEXXuGgI+OIhn/PriqQl92VokEedzShDyxQlkFVXCydoUXz1xB/o5tL/v+R3utvhl0TjtLFqx6YUI/vhQh8+iRbpTWlWDczklADhouaOxSOgibjnlo9IYfgMd4O/pAL/+DqIPGl50twdSckqw90w2nvo6BnueG8cPfl3QlYJy7E+qG19w7NJ1qGtv9iOyMVfg7hvTlI73sIMl/7B3KWYmcrw0eQAeGO6CN/Yk4NCFPKyPPI9dcVcROnVQq7qjkP6JSSvA41tPoqhCjX4OFvjy8TvgrMO/AX+fReutXxPx699m0XptiiemenMWLX12+saMii42ZnCw4tS2HYlFgkT9fcrH/ck5OH2l8ZSP/p513YhG9raFibH+DPwxMpLhvYe8cTmvHIlZxViwLRo/PD2agxQlTqMRcOZqUV3Xt6RcJGU1XOylj103bde34W4crEZAX3sLfPXEHfj1TBbe+iURadfLMX/LSdwzyBGvB3vp9IMldY4/k3Px9DcxqFRr4ONmgy/mjuywAcaO1qb4ZPZwPDLyGl7fk4DUvDIs3hGPHScy8Na0QTppuSDdi03neITOwk9dEnK7KR+HudpoC4P+Kv2e8tHcxBib5vri/g2HkJRVjBe/O4VPZg9n/3KJqVTX4vCFPEQm5WJ/Uk6jFbp9e9nC38sBkzxVXD+DmiSTyXDfUGf4DXDA+ogUbDlyGb8lZOPg+WtYNMkDj49116svQah5P8Zewb+/P41ajQC/Afb49NHhnfLl0HgPe/y2ZDw2HbyEj/+4gKOXriPow7/wxDjOoqWPOB6h8/An38DVT/m4PzkHB841nPLRVGGE8R728Pd0wMSBDga34qSLjRk+e2wEZm06hn1ns/Hh/vN4IaC/2GFRO10rqcIfyXWtBX+dv4ZK9c2ub91M5JgwoG6Fbr8BDVfoJroVC6UxXrvPCzN8e2LF7rM4ebkA7+xLxvcxV/DW/YMxum8PsUOkW9h08BLe3psEAHjAxwVrZwzt1EUNlcZyPHe3B+4f5tJgFq2fT2Xi9WAvBHqp9PqLta5CEATE1S+ixpaEDsciwQDVT/m4PykX0Wn5TUz56AB/TxXG9jP8KR99e9vi7QeG4OXvT+PD/ecxwNES9w5xEjssagVBEJCSU3qjG1HTK3T73xh0fLsVuoluZ6CjFb5bOBo/xF5F2N4kXMgtxaxNxzBtmDP+M8XT4L4skTpBEPDOvmT838FLAIAF49zxn3s9RWs1bmoWrYVfxWDiAHusnDoYbj3MRYmL6qTnlyO/rBomciN4OVuJHY7ksUgwAPVTPu5Prlu/4J9TPg50tETAjb7aQ1ykN+XjTF9XnMsuweZDqXjxu1Po1cOc09XpOXWtBidS87WFwT9X6B7a0xqTBrZ+hW6ilpDJZJgxoicCPFV4NzwZ3xxPx+74TOxPysWLgf3x2J29xA6RUPe37dUfz+D7mCsAgFeDBmLhXX304nnwz1m0/jx3DYc/OIBn/fph4YQ+Bv8FnKGq72o0yMWKXyh1AhYJeqqyBth3NhtRKdfxRzNTPvp7qjDJ0wE9u0v/m41lQQNxPrcUB1Ou4clt0djz3DiumKtnisrViEppfoXucf3sMMnTod0rdBO1lLW5AqumDcFDI1yxYs9ZnL5ShNCfE/Fd9BWEBg8UO7wuraK6Fs9tj8X+5FzIjWQImz4EM331a12cpmbR+iAyBT/GXcHKqYPgx1m0Op120LIrxyN0BhYJeib9ejn+s+s0jl6Uo/bkae12G3MFJg6o60Z0V/+uN+WjsdwIH8/ywQOfHMalvDI89XUMtj85it8k6IHC8mq8/P1p7E/ORW0zK3SP97Dj4D8SjberDXY9MxbbT6Tj3d+SkZhVjJmfn8BoByOMLq+Gg3XXep6KrahcjSe2nUR0WgGUxkb4ZPZw+HupxA6rWfWzaP1y+uYsWvO2nETQYEesuI+zaHUm7aDlXjaixtFV8K+2nrG1MMHx1HzUCjL07mGu7UY0olf3Lj/lo7WZApvm+mLaJ4cRk1aA13adxdoZQ/WiabqryiqqQMjmE9qVujtzhW6i1pAbyTDnzl4IGuyoHdB8NNcIkz88jFfuGYiZvq6S66qpj7KLKhHyxXGk5JTCytQYX8wbaRALZspkMgR7O8NvgD3WR57H1iOXse9sNg6kXMPiSR54fJx7pw607ooqqmu1U2P7cGajTsEiQc9YKI3x7oNDkJsSi/kPjoNCwW+4/q6vvQU+mT0c87acwP9irmCgkxWeGOcudlhd0oXcUoRsPo7MokqorJT4b8hIDOnJsSKk3+wslHjvIW886OOEpd+cQFa5Gq/+eAY7ozOwatpgjnfqQBevlSJk8wlcLayAykqJLx8fhQGOhrUWgaWpAivu88KMEXWzaEWnFSCsfhataYNxZx/OotVRzmYWoUYjwMFSCWd2We0ULHv10JQhjlCx9bJZd/W3x/IpXgCAt39NxIGUayJH1PXEpRfgoc+OILOoEn3su+GHp8ewQCCD4turO/49tBbL7umPbiZyxKUXIvjjQwj9KQHFlerbn4BaJT6jEDM2HsHVwgr0sat7ZhhagfB3nk51s2i9O2MobLuZ4HxuKR75/Bhe2BmP3JLK25+AWi027eYiauxB0DlYJJBBenxsb8z07QmNADy3PRYXr5WKHVKXEXUuF7M3HUdBuRrePa3x/VNjusTgeZIeuVHds2T/i364b6gTNAKw9chlTHr/AHbHXYXw97l6qc0OplzD7E3HtM+M/z01WhLPDCMjGR7ydcUfL07Ao6PcIJMBu+KuYtJ7B7DtyOUGY7So/biIWudjkUAGSSaT4a1pgzGiV3eUVNbgyW3RKCrnt38dbXfcVSzYFo0KdS3Ge9hh+5N3csEzMniO1qbYMHs4vn5iFPrYdcO1kios2RmPWZuO4UJuidjhGbQ98Vfx+NaTKK+++czoYSGtmelszE3w9gNDsPuZsRjiYo2Sqhq88VMCpm44hLgbs/FQ+wiCcHNmIxYJnYZFAhkspbEcnz02As7WpriUV4bnvo1FTa3m9gdSm2w+lIolO+NRoxEw1dsZm+eORDclhzWRdIzzsMO+JePxUmB/KI2NcOxSPu5Z/xfe2ZeM8uqa25+AGthyOBWLd9Q9M4K7wDPD29UGu58di7emDYaVqTESMosxfeMRLPvxNArKqsUOz6BlFVUit6QKciMZhriwa2tnYZFABs3eUolNc31hppDjr/N5CNuXLHZIkiMIAtb8loy3fkkEAMwb0xvrHx4GE2M+Pkh6lMZyPHe3ByKXToC/pwNqNAI+O3AR/u8fwG9ns9gFqQUEQcC7vydj5c83nxkfdpFnRv0sWn+85IcHh/eEIADfnsjA3e9HYefJdGjYBalN6rsaeTpZwsyEU593Fun/xpLkDXK2xrqZ3gDqvu3+7mSGyBFJR02tBq/8cBoboy4CAP49eQDeCPbiVJEkea625vjv3JHYFOILFxszZBZV4qmvYzF/60mkXS+7/Qm6qJpaDZb9eAaf/Fn3zHgpsH+XfGbYWSjx/kxvfLdwNAaoLFFQrsYrP5zBjM+OICGzSOzwDA4XURMHiwSShKAhTlji7wEAWL77DKIv54sckeGrVNfiqa9j8V30FRjJgHemD8GzE/txVgnqUgK8VIhcOgHPTewHhVyGqHPXEPDBQayPTEGlulbs8PRKpboWz3wTix0nM2AkA8KmD8Fzd3t06WfGHe62+GXROCy/1xPdTOSI5SxabVI/toOLqHUuFgkkGYvu9sC9QxyhrhXw1NcxuFpYIXZIBquoQo2QzScQmZQDE2MjbHxsBB65w03ssIhEYWYix0uTB+C3JXdhXD87VNdosD7yPCavP4g/z+WKHZ5eKKpQI+SLEwhPrHtmfProCMziMwMAoJAb4cm7+mD/i36Y8o9ZtPbEcxat26mqqcXZzBuLqLEloVOxSCDJMDKS4b2HvOHlZIW80mos2BbNwYZtkFNciYf/7yhOXM6Hpakxvnr8Dkwe5Ch2WESi62tvga+euAMfz/KBykqJtOvlmL/lJJ76KgaZXfhLidz6Z0ZqPiyVxvjy8Ttwz2A+M/7J0doUn8weji8fvwPuN2bRWrwjHrM3HecsWreQlFWC6hoNupsr0KuH4U+da0hYJJCkmJsYY9NcX9hZmCApqxgvfneKA8Va4dK1Ujy48QiSs0tgb6nEdwtHYxRXECXSkslkCPZ2xv4X/bBgnDvkRjL8lpAN/3UH8NmBi6iu6VozrKXmleHBz24+M3YuHM1Vh2/jrv72+G3JeLwYUDeL1tFL1xH0IWfRak7c36Y+7cpd18TAIoEkx8XGDJ89NgIKuQz7zmbjoz/Oix2SQThzpQgPfXYUVwoq0LuHOX58egw8nazEDotIL1kojfHafV74ddE4+PbqjvLqWryzLxn3fvQXjl68LnZ4neLs1SLM2HgEGfl1z4wfnhoDL2c+M1pCaSzH85PqZtGaNNAB6tq6WbQC1h3E7wnZ7IL0N7E3ZjbycbURNY6uSNQi4eDBgwgODoazszNkMhl2797dYL8gCAgNDYWzszPMzMzg5+eHhISE2573hx9+gJeXF5RKJby8vLBr164OugPSV769bfH2A0MAAOsjz2PfmSyRI9Jvh87n4ZHPj+J6WTUGu1jh+6fHwNWWzbpEtzPQ0QrfLRyNd2cMRY9uJriQW4pZm45hyY445JZUih1ehzl8IQ8P/1/dM2OQsxX+99QYuLErSKu52ppj87ybs2hdLazAwq9i8PjWk0i/Xi52eHrh5qBljkfobKIWCWVlZfD29saGDRua3L927VqsW7cOGzZswMmTJ+Ho6IiAgACUlDTfd+/o0aN4+OGHMWfOHJw6dQpz5szBzJkzcfz48Y66DdJTM31d8cQ4dwDA0u9Ocdq5Zvx8KhPzt55AWXUtxvTtgW+fvBN2ElsRlagjGRnJ8JCvK/540Q+P3ekGmQzYHZ+JSe8dwNbDqZJb5PHX01mYv+Wk9pmx4193wt6Sz4z2qJ9F69mJfaGQy/DnuWvw/+AAPow836Vn0cotqcSVggrIZMDQnlxErbOJWiQEBQVh1apVmD59eqN9giBg/fr1WL58OaZPn47Bgwdj27ZtKC8vx/bt25s95/r16xEQEIBly5Zh4MCBWLZsGSZNmoT169d34J2QvloWNBB39bdHhboWT26LxrWSKrFD0ivbjlzGoh1xUNcKmDLECVvmj4SlqULssIgMkrW5AqumDcHuZ8ZiaE9rlFTVIPTnREzdcFg7z7uh++roZTz3bSyqazW4d4gjnxk6ZGYix78nD8S+xXdhbL8eqK7R4IPIFExefxBRXXQWrfgbXY36O1jy50wEejsmITU1FdnZ2QgMDNRuUyqVmDBhAo4cOdLscUePHm1wDABMnjz5lseQdBnLjfDxLB/0set2YzGkGFTVdN1vZeoJgoB14efwxk8JEARgzp298NEsHyiNuZIlUXt5u9pg1zNj8da0wbAyNUZiVjGmf3oEr/5wGgVl1WKH1yaCIOCDiBSs2FP3zHjsTjd8PGs4nxkdoJ+DBb5+YhQ+nuUDB8u6WbTmbTmJp7+O6XKzIGnHI7jZiBpHV2UsdgDNyc7OBgCoVKoG21UqFdLS0m55XFPH1J+vKVVVVaiquvkNc3Fx3Xy8arUaanXnL3ZSf00xri1F5sbAxtnDMOPz44hJK8B/fjyNsGmDOmWWBH3MZa1GwBs/J2Fn9BUAwKKJffHcxD7Q1NZAw/rplvQxn9Q2nZHLR0Y4I2BAD6wJP49dcZnYcTIDvydk46UAD8wY7mIwqxDXagSs/CUJ357Uz2eGVH8v7/Gyx9g+Y/Hxnxfx5bF07DubjX1ns+Hewxx3D7TH3QPtMdzVBsZyvf2+t9X+mcvYtLqFUYe6WEkuv2Jq6b+l3hYJ9f75QU4QhNt+uGvtMWFhYVi5cmWj7eHh4TA3F28gVkREhGjXlqLH3GX4LMkIP8RmQpOfAT+nzps9Ql9yqdYAX543wul8I8ggYIa7Bn0rz2HfvnNih2ZQ9CWf1H6dkUs/U8B1EPC/S3JklauxfE8iNu1PwEN9atGzW4dfvl1qNMBX540QbwDPDKn+Xg4DYD8Y+CXdCOeKZEi9Xo7Nh9Ow+XAazI0FDLIRMMhWgKe1AFO9/1TXMhEREagVgPh0OQAZSlJPYW/OKbHDkozy8pYNitfbHydHx7qFWLKzs+Hk5KTdnpub26il4J/H/bPV4HbHLFu2DEuXLtW+Li4uhqurKwIDA2Fl1fnTuanVakRERCAgIAAKBfvg6cq9ALofScPqfeewJ02O4LuGY7yHXYdeU59yWVKpxtPb43E6vwAKuQzrHvLGPYOa/72gxvQpn9Q+YuTyqVoNvjqWjo/+uIjLpbV4/4wxHhvlhiWT+uplf+uSyho8sz0O8TeeGe/PGIogPVwkrav8Xj6JupwcupCHP5KvISolD4UVapzMk+FkHqCQyzDK3RZ3D6hrZXCxMRM75Fb7ey7P51Wg+tgxWCiNMW96gMG0vBmC+h4zt6O3RYK7uzscHR0REREBHx8fAEB1dTUOHDiANWvWNHvc6NGjERERgRdeeEG7LTw8HGPGjGn2GKVSCaWy8cwMCoVC1AeO2NeXoifv6osL18rwXfQVLP7uNHY/OxZ97S06/Lpi5zK3pBLzvohBYlYxLJTG+DxkBMb07dgCScrEzifpTmfmUqEAFvp54H4fV7z1ayJ+PZ1V140kIQfL7/XE/cOc9WaxqGslVZi3JRoJmcXoZiLHphBfjOmn38+MrvB7aatQYKqPK6b6uKKmVoOYtAJEJuUgMikXqXllOHThOg5duI43f02Gp5MVAjwdMMlThSEu1gb1IVuhUOBM5jUAdeMRlEoTkSOSlpb+nohaJJSWluLChQva16mpqYiPj4etrS3c3NywZMkSrF69Gh4eHvDw8MDq1athbm6O2bNna48JCQmBi4sLwsLCAACLFy/GXXfdhTVr1uD+++/Hnj17EBkZiUOHDnX6/ZH+kclkeGvaYFy8VoaYtAI8uS0au54ZC2tz6f5hSbtehjmbTyA9vxx2FibYOv8ODHbhVHJEYnG0NsUns4fjkZHX8PqeBKTmlWHJznjsOJmOt+4fDA+VpajxpV8vx5wvjiPtejl6dKt7Zgzh9JN6x1huhFF9emBUnx5YPsULF6+VIjIxB5FJOYhJK0BSVjGSsorx0R8X4GCpxCRPFQK8HDCmrx1MFfo/4Lx+RjAuoiYeUYuE6OhoTJw4Ufu6vsvP3LlzsXXrVrz88suoqKjAM888g4KCAowaNQrh4eGwtLz5AE1PT4eR0c1BO2PGjMGOHTvw2muvYcWKFejbty927tyJUaNGdd6NkV5TGsvx2WMjcP+GQ7iUV4bnd8Thi7m+khr8Ve/s1SLM23ISeaVVcLM1x5eP34HednreCZqoixjvYY/flozHpoOX8PEfF3DsUj6CPvwLC8b3waJJ/WBu0vl/ohMzizF3ywlcK6mCq60Zvnx8FNz5zDAIfe0t0HeCBRZO6Iv8smr8mZyLyKQcHEy5htySKnx7Ih3fnkiHmUKOcR52CPBUYeJAB71d46J++lMfLqImGlGLBD8/v1suPS6TyRAaGorQ0NBm3xMVFdVo24wZMzBjxgwdREhSZW+pxKa5vpix8SgOplxD2L5krLjPS+ywdOrIxTz868sYlFbVwNPJCtseHwkHS1OxwyKiv1Eay/Hc3R64f5gLVv6cgMikXHx24CJ+ir+K14O9MHmQY6d1QTp26Tqe3BaNkvpnxvyRcLDiM8MQ2XYzwYMjeuLBET1RVVOLY5fyEZmYg/1JOcgsqkREYg4iEnMgkwHDXG3g76lCgJcKHg4WetHlraC8GpfyygAAw3raiBtMF6a3YxKIOtogZ2usm+mNp7+JxeZDqRigssTMka5ih6UT+85kYfGOeFTXajDK3Rab5vrCSg8HRhJRHVdbc/x37khEJOYg9KcEXC2swFNfx8JvgD1WTh2EXj069tv8385mY9GOOFTXaHCHuy3+y2eGZCiN5ZjQ3x4T+tvjzfsHITGrGJGJda0MZ64WIS69EHHphXj393NwtTWrKxg8VRjpbguFSC3sp68UAQD62HVD924cjyAWFgnUpQUNccISfw+sjzyP5bvPoI99N/j2thU7rHb55ngaXtt9FoIATB6kwoeP+BhE/1MiAgK8VBjXzw6f/HkB/3fwIqLOXUPABwfxjF9fPDWhb4f8Ln97Ih3Ld52BRgACvVT4aBafGVIlk8kwyNkag5ytsdjfA9lFldifnIPIxBwcvngdGfkV2HL4MrYcvgxLU2P4DXCAv6cD/AY4wNqs84rG+Iy6ImEYF1ETFYsE6vIW3e2BlJwS7D2Tjae+jsGe58YZ5NRxgiDgo/0X8EFkCgBg1h2uWDVtCOQGNKMFEQFmJnK8NHkAHhjugjf2JODQhTysjzyPXXFXETp1ECYOcNDJdQRBwIY/LuD9iLpnxiMjXbFq2mBJjs+ipjlam+LRUb3w6KheKKuqm141MjEHfyTn4npZNX4+lYmfT2XC2EiGkb1t4e9V18rg1qNj15CKu1EkDHfjeAQxsUigLs/ISIb3HvLG5bxyJGYVY8G2aPzw9GhRBg22Va1GwMqfE/Dl0brVyBfd3Q8vBPTXi76lRNQ2fe0t8NUTd+CX01lY9Wsi0q6XY/6Wk7hnkCNeD/aCczu+zNDceGZsu/HMeG5iP7wYyGdGV9ZNaYzJgxwxeZAjajUC4jMK66ZXTczB+dxSHL10HUcvXcdbvySiv8oCkzxV8PdUYZirjU6/jNIIwKkb3Y182JIgKsP5FETUgcxNjLFpri/u33AISVnFePG7U/hk9nCDmFe6qqYWS787hV9PZ0EmA0KDB2HumN5ih0VEOiCTyRDs7YyJAx2wPiIFW45cxm8J2TiQcg2L/T3w+Fh3mBi37pv/6hoNXvzfKfx8KhMAEBrshXlj3TsifDJQciMZRvTqjhG9uuOVewYi7XoZIpNyEZmYgxOX85GSU4qUnFJsjLoIOwsT3D2wbj2G8R527f6CLbcCKK2qgZlCjgEiTwfc1bFIILrBxcYMnz02ArM2HcO+s9n46I/zWOLfX+ywbqm0qgYLv4rG4QvX61ZRnjkMwd7OYodFRDpmoTTGa/d54cERPbFi91lEpxXgnX3J+D7mCt66fzBG9+3RovOUVtXg6a9j8Nf5PCjkda2o9w9z6eDoydD16tENT4xzxxPj3FFUrkZUSi4ik3IRlZyLvNJqfBd9Bd9FX4GJsRHG9bODv6cKkzwdoGrD7FiXS+u+nBva05pd30TGIoHob3x72+LtB4bg5e9PY33keQxQWSJoiJPYYTUpr7QK87ecxJmrRTA3keP/5ozAeA97scMiog7k6WSF7xaOxg+xV/DOvmRcyC3FrE3HMG2YM/4zxfOW0xxfL63C/K0ncfpK3TPjs8dG4K7+fGZQ61ibK3D/MBfcP8wF1TUanLycf2PV5xxk5Ffgj+Rc/JGcC+yq+6BfXzB4OVm1qDvb5ZK69/hwPILoWCQQ/cNMX1ecyy7B5kOpWPrdKbj1MMcgZ/1abTQjvxwhX5xAal4ZbLuZYOv8kRjKuaSJugQjIxke8nVFoJcj3g1PxjfH07E7PhP7k3LxYmB/PHZnr0bfwGbkl2PuFydwKa8M3c0V2DL/DgzjSrbUTibGRhjbzw5j+9nh9fu8kJJTqi0Y4jMKcfpKEU5fKcK6iBQ4W5vC36tuHMOoPrZQGjc9g1Z9kTCc4xFExyKBqAnLggbifG4pDqZcw5PborHnuXF6syplUlYx5n5xArklVXCxMcNXT9yBPvYWYodFRJ3M2lyBVdOG4KERrnht91mcuVqE0J8T8V30Fax6YLB2Zpjk7LpnRk5x3TPjyyfuQF8+M0jHZDIZBjhaYoCjJZ6d2A+5JZU3Vn3OxV/nryGzqBJfHk3Dl0fT0M1EjgkD7OHvqcLEAQ7atRBKKmuQXVF3Pk5/Kj4WCURNMJYb4eNZPnjgk8O4lFeGp76OwfYnRzX7zUdnOZGajye2nURJZQ0GqCzx5RN3tKnPJxFJh7erDXY/OxbbT6Tj3d+SkZhVjOmfHsEjI10R4KXCCzvjUXzjmbHt8TvgaM1nBnU8B0tTPDzSDQ+PdEOluhaHL+QhMikX+5NykFtShb1nsrH3TDaMZIBvL1v4eznAXGEEATL0tDG9Zdc56hwsEoiaYW2mwKa5vpj2yWHEpBVgxe6zWPPgUNGmCAxPyMbz38ahqkaDkb27478hI2FtzhVRiahuNpo5d/ZC0GBHhO1Nxg+xV7DjZAZ2nMwAAPj26o7Nc/nMIHGYKuSY5KnCJE8VNJrBOHO16Ea3pFwkZRXjxOV8nLicr32/N7vC6QUOGye6hb72FnVTocqA76Kv4IvDl0WJY+fJdDz1dQyqajTw93TAV0+M4h97ImrEzkKJ92d647uFo7XTR04ayGcG6Q8jIxm8XW3wYuAA7Fs8HodemYiVUwdhvIcdFPK6L+EmDuCAen3AlgSi27irvz2WT/HCW78k4u1fE9HPwQITOmlGEEEQ8GnURbz7+zkAwEMjeiJs+hBOC0dEt3SHuy1+WTQO53NKMdDR0iDWfKGuqWd3c8wd0xtzx/RGfkkFdv4SjqlDHcUOi8CWBKIWeXxsb8z07QmNADy3PRYXr5V2+DU1GgFv/pKoLRCe9uuLtTOGskAgohZRyI3g5WzFAoEMhqWpMZzNwZW/9QQ/bRC1gEwmw1vTBmNEr+4oqazBk9uiUVSh7rDrVddo8MJ38dhyo3vTivu88Mo9A/ngJCIiok7BIoGohZTGdYsPOVub4lJeGZ7/Ng41tRqdX6esqgYLvozGnvhMGBvJsP7hYXhinLvOr0NERETUHBYJRK1gb6nEprm+MFPIcTDlGsL2Jev0/Pll1Zj93+M4mHINZgo5/jvXF9N8XHR6DSIiIqLbYZFA1EqDnK2xbqY3AGDzoVR8d2OKwfa6WliBGZ8dwamMQtiYK7D9yVHwG+Cgk3MTERERtQaLBKI2CBrihCX+HgCA5bvPIPpv8zu3RUpOCR789AguXSuDs7Upvn9qNHxurJZKRERE1NlYJBC10aK7PXDvEEeoawU89XUMrhZWtOk8MWn5eOizo8gurkQ/Bwt8//QY9HOw1HG0RERERC3HIoGojYyMZHjvIW94OVkhr7QaT26LRnl1TavO8UdyDh7973EUVajh42aD/y0cDWcbsw6KmIiIiKhlWCQQtYO5iTE2zfWFnYUJErOK8dL/TkGjEVp07PcxV/DklzGoVGvgN8Ae3ywYhe7dTDo4YiIiIqLbY5FA1E4uNmb47LERUMhl2HsmGx/9cf62x/zfgYt46X+nUKsRMN3HBZtCfGFuwgXQiYiISD+wSCDSAd/etnj7gSEAgPWR57HvTFaT79NoBKzem6SdOvVfd/XBew95Q8FVlImIiEiP6P0nk5KSEixZsgS9evWCmZkZxowZg5MnT97ymG+++Qbe3t4wNzeHk5MT5s+fj+vXr3dSxNRVzfR11S56tvS7U0jILGqwX12rwUvfn8LnBy8BAJYFDcR/7vWEkRFXUSYiIiL9ovdFwoIFCxAREYGvvvoKZ86cQWBgIPz9/XH16tUm33/o0CGEhITgiSeeQEJCAv73v//h5MmTWLBgQSdHTl3RsqCBuKu/PSrUtXhyWzTySqsAABXVtVj4VQx+jL0K+Y0Bzwsn9BU5WiIiIqKm6XWRUFFRgR9++AFr167FXXfdhX79+iE0NBTu7u7YuHFjk8ccO3YMvXv3xqJFi+Du7o5x48Zh4cKFiI6O7uToqSsylhvh41k+6GPXDZlFlXju21Morgbmbo3GH8m5MFUY4fM5IzBjRE+xQyUiIiJqll4XCTU1NaitrYWpqWmD7WZmZjh06FCTx4wZMwZXrlzB3r17IQgCcnJy8P3332PKlCmdETIRrM0U2DTXF5amxohJL8RbcXLEZRTBytQY3ywYhUmeKrFDJCIiIrolvZ5OxdLSEqNHj8Zbb70FT09PqFQqfPvttzh+/Dg8PDyaPGbMmDH45ptv8PDDD6OyshI1NTWYOnUqPv7442avU1VVhaqqKu3r4uJiAIBarYZardbtTbVA/TXFuDbphpuNEh8+PBQLvoxFtUYGB0sTbJk7Av1VlsyrAePvpnQwl9LBXEoHc9k5WvrvKxMEoWWTuovk4sWLePzxx3Hw4EHI5XIMHz4c/fv3R2xsLBITExu9PzExEf7+/njhhRcwefJkZGVl4d///jdGjhyJzZs3N3mN0NBQrFy5stH27du3w9zcXOf3RF1HbJ4MZwtkuM9NA1ul2NEQERFRV1deXo7Zs2ejqKgIVlZWzb5P74uEemVlZSguLoaTkxMefvhhlJaW4tdff230vjlz5qCyshL/+9//tNsOHTqE8ePHIzMzE05OTo2OaaolwdXVFXl5ebf8x+soarUaERERCAgIgEKh6PTrk+4wl9LCfEoHcykdzKV0MJedo7i4GHZ2drctEvS6u9HfdevWDd26dUNBQQF+//13rF27tsn3lZeXw9i44W3J5XIAQHP1kFKphFLZ+GtehUIh6g+p2Ncn3WEupYX5lA7mUjqYS+lgLjtWS/9t9XrgMgD8/vvv+O2335CamoqIiAhMnDgRAwYMwPz58wEAy5YtQ0hIiPb9wcHB+PHHH7Fx40ZcunQJhw8fxqJFi3DHHXfA2dlZrNsgIiIiIjIYet+SUFRUhGXLluHKlSuwtbXFgw8+iLfffltbBWVlZSE9PV37/nnz5qGkpAQbNmzAiy++CBsbG9x9991Ys2aNWLdARERERGRQ9L5ImDlzJmbOnNns/q1btzba9vzzz+P555/vwKiIiIiIiKRL77sbERERERFR52KRQEREREREDbBIICIiIiKiBlgkEBERERFRAywSiIiIiIioARYJRERERETUAIsEIiIiIiJqQO/XSRCDIAgAgOLiYlGur1arUV5ejuLiYi5LbuCYS2lhPqWDuZQO5lI6mMvOUf/5tv7zbnNYJDShpKQEAODq6ipyJEREREREuldSUgJra+tm98uE25URXZBGo0FmZiYsLS0hk8k6/frFxcVwdXVFRkYGrKysOv36pDvMpbQwn9LBXEoHcykdzGXnEAQBJSUlcHZ2hpFR8yMP2JLQBCMjI/Ts2VPsMGBlZcVfEolgLqWF+ZQO5lI6mEvpYC473q1aEOpx4DIRERERETXAIoGIiIiIiBpgkaCHlEol3njjDSiVSrFDoXZiLqWF+ZQO5lI6mEvpYC71CwcuExERERFRA2xJICIiIiKiBlgkEBERERFRAywSiIiIiIioARYJRERERETUAIsEPfPpp5/C3d0dpqamGDFiBP766y+xQ6I2CAsLw8iRI2FpaQkHBwdMmzYN586dEzss0oGwsDDIZDIsWbJE7FCoDa5evYrHHnsMPXr0gLm5OYYNG4aYmBixw6I2qKmpwWuvvQZ3d3eYmZmhT58+ePPNN6HRaMQOjW7j4MGDCA4OhrOzM2QyGXbv3t1gvyAICA0NhbOzM8zMzODn54eEhARxgu3CWCTokZ07d2LJkiVYvnw54uLiMH78eAQFBSE9PV3s0KiVDhw4gGeffRbHjh1DREQEampqEBgYiLKyMrFDo3Y4efIkPv/8cwwdOlTsUKgNCgoKMHbsWCgUCuzbtw+JiYl4//33YWNjI3Zo1AZr1qzBZ599hg0bNiApKQlr167Fu+++i48//ljs0Og2ysrK4O3tjQ0bNjS5f+3atVi3bh02bNiAkydPwtHREQEBASgpKenkSLs2ToGqR0aNGoXhw4dj48aN2m2enp6YNm0awsLCRIyM2uvatWtwcHDAgQMHcNddd4kdDrVBaWkphg8fjk8//RSrVq3CsGHDsH79erHDolZ49dVXcfjwYbbQSsR9990HlUqFzZs3a7c9+OCDMDc3x1dffSViZNQaMpkMu3btwrRp0wDUtSI4OztjyZIleOWVVwAAVVVVUKlUWLNmDRYuXChitF0LWxL0RHV1NWJiYhAYGNhge2BgII4cOSJSVKQrRUVFAABbW1uRI6G2evbZZzFlyhT4+/uLHQq10U8//QRfX1889NBDcHBwgI+PDzZt2iR2WNRG48aNw/79+5GSkgIAOHXqFA4dOoR7771X5MioPVJTU5Gdnd3g85BSqcSECRP4eaiTGYsdANXJy8tDbW0tVCpVg+0qlQrZ2dkiRUW6IAgCli5dinHjxmHw4MFih0NtsGPHDsTExCA6OlrsUKgdLl26hI0bN2Lp0qX4z3/+gxMnTmDRokVQKpUICQkROzxqpVdeeQVFRUUYOHAg5HI5amtr8fbbb2PWrFlih0btUP+Zp6nPQ2lpaWKE1GWxSNAzMpmswWtBEBptI8Py3HPP4fTp0zh06JDYoVAbZGRkYPHixQgPD4epqanY4VA7aDQa+Pr6YvXq1QAAHx8fJCQkYOPGjSwSDNDOnTvx9ddfY/v27Rg0aBDi4+OxZMkSODs7Y+7cuWKHR+3Ez0PiY5GgJ+zs7CCXyxu1GuTm5jaqpslwPP/88/jpp59w8OBB9OzZU+xwqA1iYmKQm5uLESNGaLfV1tbi4MGD2LBhA6qqqiCXy0WMkFrKyckJXl5eDbZ5enrihx9+ECkiao9///vfePXVV/HII48AAIYMGYK0tDSEhYWxSDBgjo6OAOpaFJycnLTb+Xmo83FMgp4wMTHBiBEjEBER0WB7REQExowZI1JU1FaCIOC5557Djz/+iD/++APu7u5ih0RtNGnSJJw5cwbx8fHa/3x9ffHoo48iPj6eBYIBGTt2bKOpiFNSUtCrVy+RIqL2KC8vh5FRw48xcrmcU6AaOHd3dzg6Ojb4PFRdXY0DBw7w81AnY0uCHlm6dCnmzJkDX19fjB49Gp9//jnS09Px1FNPiR0atdKzzz6L7du3Y8+ePbC0tNS2EFlbW8PMzEzk6Kg1LC0tG40l6datG3r06MExJgbmhRdewJgxY7B69WrMnDkTJ06cwOeff47PP/9c7NCoDYKDg/H222/Dzc0NgwYNQlxcHNatW4fHH39c7NDoNkpLS3HhwgXt69TUVMTHx8PW1hZubm5YsmQJVq9eDQ8PD3h4eGD16tUwNzfH7NmzRYy6CxJIr3zyySdCr169BBMTE2H48OHCgQMHxA6J2gBAk/9t2bJF7NBIByZMmCAsXrxY7DCoDX7++Wdh8ODBglKpFAYOHCh8/vnnYodEbVRcXCwsXrxYcHNzE0xNTYU+ffoIy5cvF6qqqsQOjW7jzz//bPJv5Ny5cwVBEASNRiO88cYbgqOjo6BUKoW77rpLOHPmjLhBd0FcJ4GIiIiIiBrgmAQiIiIiImqARQIRERERETXAIoGIiIiIiBpgkUBERERERA2wSCAiIiIiogZYJBARERERUQMsEoiIiIiIqAEWCURE1GGioqIgk8lQWFgodihERNQKXEyNiIh0xs/PD8OGDcP69esBANXV1cjPz4dKpYJMJhM3OCIiajFjsQMgIiLpMjExgaOjo9hhEBFRK7G7ERER6cS8efNw4MABfPjhh5DJZJDJZNi6dWuD7kZbt26FjY0NfvnlFwwYMADm5uaYMWMGysrKsG3bNvTu3Rvdu3fH888/j9raWu25q6ur8fLLL8PFxQXdunXDqFGjEBUVJc6NEhF1AWxJICIinfjwww+RkpKCwYMH48033wQAJCQkNHpfeXk5PvroI+zYsQMlJSWYPn06pk+fDhsbG+zduxeXLl3Cgw8+iHHjxuHhhx8GAMyfPx+XL1/Gjh074OzsjF27duGee+7BmTNn4OHh0an3SUTUFbBIICIinbC2toaJiQnMzc21XYySk5MbvU+tVmPjxo3o27cvAGDGjBn46quvkJOTAwsLC3h5eWHixIn4888/8fDDD+PixYv49ttvceXKFTg7OwMAXnrpJfz222/YsmULVq9e3Xk3SUTURbBIICKiTmVubq4tEABApVKhd+/esLCwaLAtNzcXABAbGwtBENC/f/8G56mqqkKPHj06J2gioi6GRQIREXUqhULR4LVMJmtym0ajAQBoNBrI5XLExMRALpc3eN/fCwsiItIdFglERKQzJiYmDQYc64KPjw9qa2uRm5uL8ePH6/TcRETUNM5uREREOtO7d28cP34cly9fRl5enrY1oD369++PRx99FCEhIfjxxx+RmpqKkydPYs2aNdi7d68OoiYion9ikUBERDrz0ksvQS6Xw8vLC/b29khPT9fJebds2YKQkBC8+OKLGDBgAKZOnYrjx4/D1dVVJ+cnIqKGuOIyERERERE1wJYEIiIiIiJqgEUCERERERE1wCKBiIiIiIgaYJFAREREREQNsEggIiIiIqIGWCQQEREREVEDLBKIiIiIiKgBFglERERERNQAiwQiIiIiImqARQIRERERETXAIoGIiIiIiBpgkUBERERERA38P+i94fa5H5zQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, \n",
    "        10.1, 9.9, 10.2, 10.0, 9.9, 11.4]\n",
    "plt.plot(data)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('position');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After a period of near steady state, we have a very large change. Assume the change is past the limit of the aircraft's flight envelope. Nonetheless the Kalman filter incorporates that new measurement into the filter based on the current Kalman gain. It cannot reject the noise because the measurement could reflect the initiation of a turn. Granted it is unlikely that we are turning so abruptly, but it is impossible to say whether \n",
    "    \n",
    "* The aircraft started a turn awhile ago, but the previous measurements were noisy and didn't show the change.\n",
    "      \n",
    "* The aircraft is turning, and this measurement is very noisy\n",
    "    \n",
    "* The measurement is very noisy and the aircraft has not turned\n",
    "\n",
    "* The aircraft is turning in the opposite direction, and the measurement is extremely noisy\n",
    "\n",
    "\n",
    "Now, suppose the following measurements are:\n",
    "\n",
    "   11.3 12.1 13.3 13.9 14.5 15.2\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n",
    "plt.plot(data + data2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given these future measurements we can infer that yes, the aircraft initiated a turn. \n",
    "\n",
    "On the other hand, suppose these are the following measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n",
    "plt.plot(data + data3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Overview of How Smoothers Work\n",
    "\n",
    "The Kalman filter is a *recursive* filter with the Markov property - it's estimate at step `k` is  based only on the estimate from step `k-1` and the measurement at step `k`. But this means that the estimate from step `k-1` is based on step `k-2`, and so on back to the first epoch. Hence, the estimate at step `k` depends on all of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n",
    "\n",
    "Smoothing filters incorporate future measurements into the estimate for step `k`. The measurement from `k+1` will have the most effect, `k+2` will have less effect, `k+3` less yet, and so on. \n",
    "\n",
    "This topic is called *smoothing*, but I think that is a misleading name. I could smooth the data above by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types of Smoothers\n",
    "\n",
    "There are three classes of Kalman smoothers that produce better tracking in these situations.\n",
    "\n",
    "* Fixed-Interval Smoothing\n",
    "\n",
    "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed-interval smoother will collect all the data, then estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n",
    "\n",
    "\n",
    "* Fixed-Lag Smoothing\n",
    "\n",
    "Fixed-lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will ingest the first 3 measurements but not output a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurements 1 through 4 into account. When the 5th measurement comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account. This is useful when you need recent data but can afford a bit of lag. For example, perhaps you are using machine vision to monitor a manufacturing process. If you can afford a few seconds delay in the estimate a fixed-lag smoother will allow you to produce very accurate and smooth results.\n",
    "\n",
    "\n",
    "* Fixed-Point Smoothing\n",
    "\n",
    "A fixed-point filter operates as a normal Kalman filter, but also produces an estimate for the state at some fixed time $j$.  Before the time $k$ reaches $j$ the filter operates as a normal filter. Once $k>j$ the filter estimates $x_k$ and then also updates its estimate for $x_j$ using all of the measurements between $j\\dots k$. This can be useful to estimate initial paramters for a system, or for producing the best estimate for an event that happened at a specific time. For example, you may have a robot that took a photograph at time $j$. You can use a fixed-point smoother to get the best possible pose information for the camera at time $j$ as the robot continues moving.\n",
    "\n",
    "## Choice of Filters\n",
    "\n",
    "The choice of these filters depends on your needs and how much memory and processing time you can spare. Fixed-point smoothing requires storage of all measurements, and is very costly to compute because the output is for every time step is recomputed for every measurement. On the other hand, the filter does produce a decent output for the current measurement, so this filter can be used for real time applications.\n",
    "\n",
    "Fixed-lag smoothing only requires you to store a window of data, and processing requirements are modest because only that window is processed for each new measurement. The drawback is that the filter's output always lags the input, and the smoothing is not as pronounced as is possible with fixed-interval smoothing.\n",
    "\n",
    "Fixed-interval smoothing produces the most smoothed output at the cost of having to be batch processed. Most algorithms use some sort of forwards/backwards algorithm that is only twice as slow as a recursive Kalman filter. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-Interval Smoothing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many fixed-lag smoothers available in the literature. I have chosen to implement the smoother invented by Rauch, Tung, and Striebel because of its ease of implementation and efficiency of computation. It is also the smoother I have seen used most often in real applications. This smoother is commonly known as an RTS smoother.\n",
    "\n",
    "Derivation of the RTS smoother runs to several pages of densely packed math. I'm not going to inflict it on you. Instead I will briefly present the algorithm, equations, and then move directly to implementation and demonstration of the smoother.\n",
    "\n",
    "The RTS smoother works by first running the Kalman filter in a batch mode, computing the filter output for each step. Given the filter output for each measurement along with the covariance matrix corresponding to each output the RTS runs over the data backwards, incorporating its knowledge of the future into the past measurements. When it reaches the first measurement it is done, and the filtered output incorporates all of the information in a maximally optimal form.\n",
    "\n",
    "The equations for the RTS smoother are very straightforward and easy to implement. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future. Here is it very important to distinguish between past, present, and future so I have used subscripts to denote whether the data is from the future or not.\n",
    "\n",
    "    Predict Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{P} &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n",
    "\\end{aligned}$$\n",
    "\n",
    "    Update Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F}^\\mathsf{T}\\mathbf{P}^{-1} \\\\\n",
    "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{k+1} - \\mathbf{Fx}_k) \\\\\n",
    "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{k+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "As always, the hardest part of the implementation is correctly accounting for the subscripts. A basic implementation without comments or error checking would be:\n",
    "\n",
    "```python\n",
    "def rts_smoother(Xs, Ps, F, Q):\n",
    "    n, dim_x, _ = Xs.shape\n",
    "\n",
    "    # smoother gain\n",
    "    K = zeros((n,dim_x, dim_x))\n",
    "    x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy\n",
    "\n",
    "    for k in range(n-2,-1,-1):\n",
    "        Pp[k] = F @ P[k] @ F.T + Q # predicted covariance\n",
    "\n",
    "        K[k]  = P[k] @ F.T @inv(Pp[k])\n",
    "        x[k] += K[k] @ (x[k+1] - (F @ x[k]))     \n",
    "        P[k] += K[k] @ (P[k+1] - Pp[k]) @ K[k].T\n",
    "    return (x, P, K, Pp)\n",
    "```\n",
    "        \n",
    "This implementation mirrors the implementation provided in FilterPy. It assumes that the Kalman filter is being run externally in batch mode, and the results of the state and covariances are passed in via the `Xs` and `Ps` variable.\n",
    "\n",
    "Here is an example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise\n",
    "import kf_book.book_plots as bp\n",
    "\n",
    "def plot_rts(noise, Q=0.001, show_velocity=False):\n",
    "    random.seed(123)\n",
    "    fk = KalmanFilter(dim_x=2, dim_z=1)\n",
    "\n",
    "    fk.x = np.array([0., 1.])      # state (x and dx)\n",
    "\n",
    "    fk.F = np.array([[1., 1.],\n",
    "                     [0., 1.]])    # state transition matrix\n",
    "\n",
    "    fk.H = np.array([[1., 0.]])    # Measurement function\n",
    "    fk.P*= 10.                     # covariance matrix\n",
    "    fk.R = noise                   # state uncertainty\n",
    "    fk.Q = Q_discrete_white_noise(dim=2, dt=1., var=Q)  # process uncertainty\n",
    "\n",
    "    # create noisy data\n",
    "    zs = np.asarray([t + randn()*noise for t in range (40)])\n",
    "\n",
    "    # filter data with Kalman filter, than run smoother on it\n",
    "    mu, cov, _, _ = fk.batch_filter(zs)\n",
    "    M, P, C, _ = fk.rts_smoother(mu, cov)\n",
    "\n",
    "    # plot data\n",
    "    if show_velocity:\n",
    "        index = 1\n",
    "        print('gu')\n",
    "    else:\n",
    "        index = 0\n",
    "    if not show_velocity:\n",
    "        bp.plot_measurements(zs, lw=1)\n",
    "    plt.plot(M[:, index], c='b', label='RTS')\n",
    "    plt.plot(mu[:, index], c='g', ls='--', label='KF output')\n",
    "    if not show_velocity:\n",
    "        N = len(zs)\n",
    "        plt.plot([0, N], [0, N], 'k', lw=2, label='track') \n",
    "    plt.legend(loc=4)\n",
    "    plt.show()\n",
    "    \n",
    "plot_rts(7.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've injected a lot of noise into the signal to allow you to visually distinguish the RTS output from the ideal output. In the graph above we can see that the Kalman filter, drawn as the green dotted line, is reasonably smooth compared to the input, but it still wanders from from the ideal line when several measurements in a row are biased towards one side of the line. In contrast, the RTS output is both extremely smooth and very close to the ideal output.\n",
    "\n",
    "With a perhaps more reasonable amount of noise we can see that the RTS output nearly lies on the ideal output. The Kalman filter output, while much better, still varies by a far greater amount."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zuH07Hxi9Qa/2T6gq+YKRElTQpUQfLCw0WyVKcJ7xJEAXQgghhEhHe/bsoX379qhUqmTL58yZg0KhwM/PL9nyqKgomjZtyuHDh3XO+/v707NnT4YPH05oaGiSt4M6O1cEfLh3rzVgBEZvoJwXuC9FZR6nqfQEqkZXxXe5b2qHKdKQ5KALIYQQQqQTtVrNoEGDtMF569atOX/+PAEBAYwfPx5DQ0MAZs+ezd27d5Nto2/fvjrBeaFChbC2ttYev379WhucGxoaUqpUJ3LnPs29e6e5d68jhoZG1PY8jPFQO6g3D8zjIAQK+hdkqftSjqw8ou2H+DLICroQQgghRDo5ffq09s2cFSpU4I8//kBPT7M+OnLkSNRqNaNGjQJgyZIlTJw4Uef6hw8fsmbNGgCyZctGs2bN2L9/f5LdWMCAEiV+4t49Hy5dygNAbhs1ffso6NsXTK3LkH+mAQ7ZnBlYbiCdSnbC0twy/QYuUkUCdCGEEEKIdHLz5k3t544dO2qD87c6deqkDdDfrfvWxo0btavvMTExrF27Vqc8R46ChIS0Bn7h2jXN2zhLVHiFY/vpxGY/z1jPfSgUCsCK492OUyx3MdmVJROQ/0NCCCGEEOnEyMhI+zkkJCRJ+bvn3q0bFxfHhg0bmDZtmvbc20DdwMCA/Pk9iIsbxZMnldC81TMRp5KHqDDgL3a+mM+1iGiIgGMPj1HDqQYAJW1LpvHoRHqRHHQhhBBCiHRStWrV/69gw8KFC3n16pW2TKVS6aS0VK9enefPnzNmzBgcHR3p0qULL1680JabmVlQseIoTEwCuX9/F0+eVMbEJA4sR0HD7DxpVZ8Nj6cTrYymbJ6y/NnuT6rlr/b5BivSjKygCyGEEEKkEycnJ5o0acKOHTt48eIF33zzDT179iRnzpysW7eOM2fOAGBmZsbx48cZOHAgCQkJ77ViDnQnOvp3zpwxA8De/g2dOgWzYHslYtu+AH1IACrnq8yo6qNo4NxA+4OByHwkQBdCCCGESEezZ8/G39+fZ8+e8eLFC3799dckdaKjo9m4caP2WF9fn9KlWxEa6sP9++5o0lgA9uLiugNFwkGmTLmlOR0MOU1z8ofXH9QuUFsC86+ABOhCCCGEEOnI0dGRkydP4u3tzc6dOz/4FlCA7NlzUqxYb27c6Mv58/kAMDNTY2a2idcGQ6DqA+46Am+3LVfDN/7fcHjXYXLkyJH+gxGfhQToQgghhBDpLH/+/IwaNQp9fX127NiR5KVCLi5uZM/+A/7+7Tl50hQAR0fo3x+KN/ybWRcWse/Bg38ucIaC8QXp06cP/fr1w8zM7HMOR6QzCdCFEEIIIdJJfHw8mzdvxtfXl9OnT+uU6evrU7ZsCyIjfbh5sypv01iqVQMfHzXGJXYz+dTvDNn8NwB6Cj3aFW9HL9dePHV+Sps2bXR2fhFfDwnQhRBCCCHSWFBQEAsXLmTu3Lk8f/5cpyx79hyULNmLW7f6cvasIwBGRtChA/zwA5QuDbdf36HonMaaMn0jupXqxmD3wRTKUQilUsmuO7sk1/wrJgG6EEIIIUQa8ff3x8/Pj3Xr1hEfH69T5uLyDTY2Ppw715FjxzRpLHZ20LcvdP0+joD4U5R2qglAkVxF6FSyE3nM8/Bj5R+xt7D/3EMRGUgCdCGEEEKIVFAqlWzduhVfX19OnDihU6anp0f58s2JifHhypXq3L2rWfUuV06zWt6wWSTLri6g0rrpvIp+xX2f+zhaaVbVV7dc/dnHIr4MEqALIYQQQqTAq1evWLRoEXPnzuXp06c6ZdbW2SlVqid37nhx5kx+APT1oXVrTWDu8k0wfmd98ZnrR2hsKAB5LfISEBqgDdBF1iUBuhBCCCHEJ7h06RK+vr6sXbuWuLg4nTJn5+LkyePDuXOdOXJEs7NKzpzQu7cmlcUqdyS/Hf8Nv1l+RCujASicszBDqwyl8zedMdKXhz6FBOhCCCGEEP8pISGBlStXMn78eB68u90hoFAoqFDhW+Ljfbh4sRb37mnSWL75RrNa3qEDmGpSznkWGcmcc3OIVkZT2q40w6sOp2Wxlujr6X/uIYkvmAToQgghhBAfEBwczOLFi5k6dSqvX79OpkYZDA39OHPGHQA9PWjeHHx8oHp1UCjgUfgjHE01aSv2Fvb4NvAlp1lOmhZuKjuxiGRJgC6EEEII8Z4rV67g5+fH6tWriY2Nfa/UCGgOzATyEB8P+voRDBhgjre3Hvk1KeeExYYx+vBo5p6by97Oe6lTsA4A3Up3+2zjEJmTXkZ3QAghhBDiS5CQkMDWrVupVasWbm5uLF68+L3g3AZr67lALPAHkAcDg9tAbxIT81C58lby5weVWsXSi0sp7FcYv7N+JKoT2Xd/X4aMSWROsoIuhBBCiCwtJCSEJUuWMGfOHB4+fKhTZm5uwZs3hYCpQB3CwjRpK40ba/LL4+MDaNx4IQDLli3DsZIj/Xf35+zTswAUy1UMv4Z+2tVzIT6GBOhCCCGEyJKuXbuGn58fq1atIiYmRqesQIEiODj4cPZsByA7AEZG0fTvb4aXFxQqpKmnUtXH1NSUmJgYTpuepuLiiqhRY2FkwdiaY/Gu4I2hvuFnHpnI7CRAF0IIIUSWkZiYyM6dO/H19eXQoUNJysuVa4Ra7YO/vwcPHrzNBL4B+FGvXhjTpq3Tqf/q1SttcG8RY0EwwXz3zXdMqjuJPBZ50nk04mslAboQQgghvnqhoaEsXbqU2bNnExgYqFNmYWFBqVLdePiwP+fPuwCaNJamTaFPHyWenrV49SqI3bv1OXNmABUrVgTg+MPj/Db9N207bUu0pWPvjrjZuX22cYmvkwToQgghhPhq3bhxAz8/P1auXEl0dLROWf78Ljg6euPv78nx45YAWFlBjx7Qrx8ULAhgSN++ffjll19ITEykWrVqNGzfkIACAVzTuwbGgAkYJBjQp3cfCtgV+OxjFF8fCdCFEEII8VVJTExk165d+Pr6cuDAgSTlZco0QK324eLF+jx8qEljcXUFb2/o3BnMzXXrDx8+nCNHj3DswTGUFZVsL7Bdsw+eGripqTN//nwKFJDgXKQNCdCFEEII8VUIDw9n2bJl+Pn5ERAQoFNmbm6Om1tXHj7sz4ULRYB/0lh8fKB2bc1xci69vkR4u3AIeudkAHAAytiV4ZdNv9C4ceP0GZTIkiRAF0IIIUSmduvWLWbPns3y5cuJiorSKXNwKES+fN5cvNiVEyesAMieHbp3By+vt2ksSanVau1bPrObZOdy0GVMDUxp79qeakbVsClnQ/7B+SlevLi8DVSkOQnQhRBCCJHpqFQq9uzZg6+vL3v37k1S7uZWj4QEH65fb8jjx5o0lm++0aSxdOwIZmZJ21Sr1Zx+chrfs77oK/RZ3XI1AEVyFWF9q/XULViXnGY503VcQoAE6EIIIYTIRCIiIli+fDl+fn7cu3dPp8zMLBslSngSGNify5eLAaCvD61aQf/+ULVq8mkscQlxbLyxEd8zvpx7dk5znUKf6fWnY5PNBoB2Jdql78CEeIcE6EIIIYT44t25c4fZs2ezbNky3rx5o1Nmb18AO7v+XL3anbNnrQGwsYHevTV/8ubV1FOpVOzdu48tW7YQEhKCRR4LFOUV7AraxcuolwAY6xvTsWRHvCt4a4NzIT43CdCFEEII8UVSqVTs27cPX19fdu/enaTc1bUO8fE+3LvXmGfP9AGoVEmzWt66NRgb/1M3ICCAFi1acOXKlX9OVgZyaT7myZaH/hX707NMT3Jny52OoxLiv0mALoQQQogvSmRkJCtWrMDPz487d+7olJmYmFKsWBcCA725caM4oAnE27fXBOblyiVt787jO7h/705wkWAwAs7/v+Ai4AL4Qy6DXAzwGoBZcsnpQnxmEqALIYQQ4rNRqVScOHGCO3fucPv2bcqVK0fe/+eg3Lt3jzlz5rB06VIiIiJ0rrO1zU+uXP25caM7Fy/mAMDBAfr2he+/h9zvLXoHhAaw7dY2tt/ZztEHR1HXUANgmsuU1cNXU6ZMGY4fP86wYcN49uwZV7nKkiVL8Pb2Tv9JEOI/fFKAPm/ePObNm6d9RW7x4sUZPXo0DRs2BDRPP48bN46FCxcSGhpKxYoVmTNnDsWLF0/zjgshhBAic9m4cSMjRozQebhzxowZ1KxZE319ffbt24darda5xsWlFlFRPjx71pSXLzVpLLVra970+e23YPBeJKNSq6i0uJL2YU8AFMBL0Lurxx8T/6Bp2aYAODk5UaxYMcqXLw/A4sWLJUAXXwS9T6mcL18+Jk6cyPnz5zl//jy1a9emWbNmXL9+HYDJkyczffp0Zs+ezblz57Czs8PDw4PIyMh06bwQQgghMod58+bRtm3bJDuvJCQkcODAAfbu3asNzo2NTShatCemple4e/cQz541x8JCn/794cYNOHgQWraEBGLZdXcX446M07anp9DD1twWfYU+tZxq8WuVX2EWMA9qqWtpg/O3ypUrR7Fimh1fbty4keQHBCEywietoDdtqvtF/dtvvzFv3jxOnz6Nq6srM2fOZOTIkbRs2RKAFStWYGtry9q1a+ndu3eybcbFxREXF6c9fvsrLaVSiVKp/KTBpIW398yIe2d2MnepI/OXcjJ3KSdzl3Iydx/v4cOH+Pj4aI/z5s1LcHAwsbGxOvWMjbOTJ89QAgO/59YtzX7jxYqp8fJS0b5DAq8TH3D91XU2HL7GhRcXOPjgIFFKzYuJOhTvQAHrAgBMrj2ZxY0Xk8M0B6GhoYwKHQVAWFhYkv9fKpWK8PBwAAwMDEhISEifSUhD8rWXchk9dx97X4U6hT8qJiYmsnHjRjw9Pbl48SImJiYUKlSICxcuULp0aW29Zs2aYW1tzYoVK5JtZ+zYsYwbNy7J+bVr18qDGkIIIcRXYPXq1WzatOlfauQHRgLdAH0Uls8oVv0YLSrkoFzJWBQKWPN8DRtfbkxyZU7DnJS3LE8LmxbYGtsm27q3tzePHz8G4JdffuGbb77Rlh05coSZM2cC4ObmlmxMIkRaiY6OpmPHjoSHh2NpafnBep/8kOjVq1epXLkysbGxmJubs3XrVlxdXTl58iQAtra6fzlsbW15+PDhB9sbPnw4AwcO1B5HRETg4OBAvXr1/rXj6UWpVLJ//348PDwwNDT87PfPzGTuUkfmL+Vk7lJO5i7lZO7+W1RUFGvXruWvv/5KUmZoaIx1jiYE6zVGZR8PtpfBpjrGDreI0w/lBjCt3W7qFGgEQPj1cLbv3E6xXMUonrs4xXMXp7ZTbUrblUaR3NuH3vHo0SPtCv5vv/1Gt27dtA+JrlmzRltv1KhRNGrUKO0mIJ3I117KZfTcvf/w84d8coBepEgRLl26RFhYGJs3b8bT05OjR49qy9//S6JWq//1L46xsTHG725U+n+GhoYZ+kWX0ffPzGTuUkfmL+Vk7lJO5i7lZO6SCgwMZM6cOSxevJiwsDCdMiurvJiY9OPly568st8OzbrrlMehySN3zuGMUq3Uzm37ku3p+E1HDPQ+fQO6Pn36sHPnTvbt20dcXBzz589PUqdz5860bNnyP4P9L4l87aVcRs3dx97zk7/KjYyMcHZ2BjQPVpw7d45Zs2YxdOhQAF68eEGePHm09YOCgpKsqgshhBDi66JWqzly5Ah+fn5s27YNlUqlW8HYHkrnIzxsIOG32mFmpqaEU04CTfISeT+EmMAYCIIdi3dQx60OpoamOpcb6RuluG+GhoZs27aNoUOHsmjRImJiYrRlVlZW/PDDD4wePTpTBefi65bqfdDVajVxcXEUKFAAOzs79u/fr81Bj4+P5+jRo0yaNCnVHRVCCCHElyc6Opq1a9fi6+vL1atXdcoMDIwwdSxFZLkgcA0EnkHgdFqXsGf0aCf27LnDwYMl2Lt3LwB16tShSbkm6dJPExMTZs2axbhx49i7dy8hISHY2NjQoEEDsmXLli73FCKlPilAHzFiBA0bNsTBwYHIyEjWr1/PkSNH2LNnDwqFggEDBjBhwgRcXFxwcXFhwoQJmJmZ0bFjx/TqvxBCCCEywKNHj5g7dy6LFi0iJCREp8zMIjfxTo4k1LlOpPVZABTxpqgvZ4fzZ9n0sjrvPzNqbGzMb7/9lu79tra2pl27dul+HyFS45MC9JcvX/Ldd9/x/PlzrKys+Oabb9izZw8eHh4ADBkyhJiYGLy8vLQvKtq3bx8WFhbp0nkhhBBCfD5qtZrjx4/j6+vL1q1bk6Sx5MjhTmioD9GtZoHTKQBs1CX4oUpfupdriXcvbza9TLqbS44cOVi3bh0VK1b8LOMQ4kv3SQH6kiVL/rVcoVAwduxYxo4dm5o+CSGEEOILEhMTw7p16/D19eXy5cs6ZXr6hug7OKN87ktISF0Aikfpkd2qAL9+25caBapoc7s3btyIv78/y5YtIyAggLCwML777ju6dOnyUWkmUVFRrFq1irVr1/Ls2TOsra1p3rw5PXv2lOfdxFcl1TnoQgghhPg6PX78mHnz5rFw4UKCg4N1Cw3MoHhuVB4PUZnfxOioP71L1KVvXyhWrA3QJtk2y5YtS9myZVEqlezatYtGjRp91M4Wt27dokGDBkm2bvb392fy5Mls3LiR+vXrp3SoQnxRJEAXQgghspCEhAR2797N2bNnUavVlCpVim+//RYjI80uKWq1mhMnTuDr68uWLVtITEzUbSCHFVSLhZLRYPAQVHpwOx9GQdPo06cpxYq5pnmfw8LC8PDw4MmTJ9pzVlZW2jeARkZG0rx5c86cOaPzEiIhMisJ0IUQQogsYu/evfTq1YtHjx7pnLe1tWXatGkolUp8fX25ePGiTrmeniEqmoDnTsivCYqNovNRMq4sr/Zc5NHVR7xBs9/4sWPH0rzfixYt0gbnbm5uLF26lDJlyhAYGIiPjw87duwgNjaWiRMnsnbt2jS/vxCfmwToQgghRBawf/9+mjRpQkJCQpKyly9f0rlz5yTnFWZGqKOHo1L1BvLAy87kjA1m1bAxNChZEYVCQeSoSEqXLs39+/c5fvw4V69epWTJkmna95UrV2o///HHHxQpUgQAJycn1q9fT/78+Xn9+jWbNm1i0aJFsm2iyPT0MroDQgghhEhfiYmJ9O7dWxucV69enfHjx1O1atXkX85jD7QA9cB4FLk64eDwHGgAu9byp9dIGn5TSXudhYUFffv21V76999/p3n/3+adFypUSBucv2VmZkatWrUAzWvcX7x4keb3F+JzkwBdCCGE+Mrt37+fBw8eAFC4cGGio6P5+eef+fvvv1Gr1ZpKekAJoAfQwQYz/X504RgB5wtRvfp0YC+gxtLSMkn7755LboU+td5u1/z8+XPevHmTpPzu3bvaz+bm5ml+fyE+NwnQhRBCiK/c4cOHtZ/v3LnD+fPntccKQ0uoDvTODk69yXVlBesrPCNs7WxW/FoNp/x6FC9eXFv/3XQT0DxU+u65d+umlYYNGwKat5aOHj36nx8qgNWrV3Pp0iUASpcuLdstiq+CBOhCCCFEBlCpVMTExOgEm2ntzJkzdOrUialTpyYpUyjKACtQqwIxCd4FC0bCziN0qHSedm31eXfnw65du2JgoHlsbfr06QwePJhr165x6tQp2rRpo01rcXZ2pmbNmmk+Dm9vb21KzYwZMyhZsiQ+Pj7UrFmT7777TltvwIABaX5vITKCBOhCCCHEZ3T48GGaNWuGiYkJZmZm5M6dm4EDBybZWSWl4uPjWbNmDRUrVqRSpUqsXbv2nzd+KoDiQPX6qNXnKVeuC4sXWFOv0EpQ/QTcply5cknazJMnDyNHjgQ0K+ZTp06lZMmSuLu7s3nzZk3TCgUzZsxATy/tQws3Nzd8fX21x9evX8fPz4+jR49qz33//fc6wboQmZkE6EIIIcRn8uuvv1K7dm22b9+OUqkEIDg4mBkzZuDm5sapU6dS3PbLly8ZN24c+fPnp3Pnzpw9e/afQlOgkilU7QMvLmJ/z4epU48wbtwudu5syfbt6wHInj07rVu3Trb9MWPGMHr0aPT19ZOUWVpasn79epo0aZLi/v+X/v37s3PnTipXrqxz3sXFRfsypWQfeBUiE5JtFoUQQojPYNOmTYwePVp7bGdnh7OzM+fOnSMuLo6wsDCaNm3K7du3yZkz50e3e+7cOfz8/Fi/fr026NeyBQoVhbDhOL5sxOPAcajVNXhGBD/9lLQtPz8/zMzMkr2PQqFg3Lhx9OrVixUrVnDt2jUMDAyoUqUKHTt21D7ImZ4aN25M48aNefDgAc+fP8fa2pqiRYumy6q9EBlJAnQhhBDiM5g0aZL286+//sqwYcMwMDDg1atXtG3bliNHjhAcHMySJUsYMmTIv7alVCrZvHkzs3xncfrU6fdK9YCWYN4aA0Up2hcsQp8+4O4Ou3Y1oFevLTx7FqFzRc6cOfH19aVjx47/OY68efMyYsSIjx12uihQoAAFChTI0D4IkZ4kQBdCCCHSWWBgoHbnlFKlSjFy5EhtOkbu3LlZuHAhhQsXBmDDhg0fDNCDgoLwm+vH3HlzCQkK0S00BXLUhKcrcHZ2pE8f8PSEXLn+qdK4cWMCAwPZsWMHZ86cQaVSUbp0aVq2bImJiUlaD1sIkUISoAshhBDp7NWrV9rPlSpVSpIr7eLiQq5cuXj9+jWvX7/WKVOr1Vy8eBFfX1/WrluLMv69NJbc+pC7NnqvptCysht9+kCtWvChrA9DQ0NatmxJy5Yt02RsQoi0JwG6EEIIkc5yvbOMfebMGdRqtU6Qfu/ePW1gnj13dg49OMSBuwfYsnULoUdDCboZpNugArB1AmNP8imG0qejKd27Q548n2EwQoh0JwG6EEIIkc6cnJwoW7Ys/v7+XLx4kYkTJzJ48GAMDAx4/fo17Qa3gxqAE1y1uUqd7+vAOSDy/ZasQf87FKqBNC7nRO/e0LAhJLOxihAiE5PHnoUQQoh0plAoGDp0qPZ4xIgR5M+fnxo1auDg4MAF2wtQFLgMidMT4RDvBefFgQXY2j5h1AhfAgOd2LEDmjSR4FyIr5EE6EIIIcRn0KZNG0aOGQllge7wLOgZx44dIzY2FtYBC4BLQOLbKxRAM+Ag9epdZcuWXjx+nI0GDU4ybFhH7O3tyZkzJ5UrV2bx4sWadoQQXwVJcRFCCCHSWbQymsUXFrPccjk0BaIBO+DJ/yvo7HpoBXxPzpxe9OxZkJ49oWBBzcOiI0eO5Pfff9dp+/Tp05w+fZrZs2ezd+9ebG1tP8OIhBDpSQJ0IYQQIp1ExkUy99xcpp2axqvoV/ACzC6aobyoTLobC8UAH6pX70y/fuY0bw5GRv+ULliwQCc4t7CwwMrKiidPNFH+5cuXad68OSdOnJAX9wiRycnfYCGEECIdBEcH4zTLiWH7hvHK/xUmq01gPkSfiX4nOFcATbGw2M/Agde5fbsPR4+a07atbnCekJDAb7/9pj2eNGkSr1694vHjx5w4cYK8efMCmtX0gwcPfr5BCiHShQToQgghRBqJVkZrPytiFdhessVgjgH8AbH33s0RtwR+pFy5u6xevZ2goLpMm6bg/+8qSuL48ePalfLGjRszZMgQjI2NAXB3d2fGjBnauqtXr07rYQkhPjNJcRFCCCFS6UnEE6aenMryS8vZVGMTG5dvZNWqVcTExLxXswimpj507fod/ftb4Or6ce0/e/ZM+7lOnTpJyt89925dIUTmJAG6EEIIkUIv4l7gtcuLFZdXoLyphDPgMdwjmZqNcHX1YfBgD9q108PU9NPuY21trf189erVJOXvnrOysvq0xoUQXxwJ0IUQQohPEJsQy4pLK9h8YzMHbhxAfVENZ4Gw92taYGTUjXbt+jNkiAslSqT8njVq1MDCwoLIyEhWr16Np6cnNWrUACA0NFRnj/XmzZun/EZCiC+CBOhCCCHEf4iMi8TC2AIAhVrBjyt/JOZUDFwG3t+MBRecnLwZMsQTT09LzMxSf39zc3N69+7N1KlTUSqV1KxZk+rVq2NjY8PevXuJjNS81Shfvny0bt069TcUQmQoCdCFEEJkOgkJCRw8eJC7d+9iampK7dq1KVCgQJre49brW2y5uYXNNzcTGhPKnX53WL58OT/++CMxb97PLQfwoE6d3kyd2oJSpdJ+D4bx48dz5coV9u3bB8CxY8d0yrNnz86ff/6JiYlJmt9bCPF5SYAuhBAiU1mzZg3Dhw/n8ePH2nMKhYLGjRszb9488uXLl6J21Wo1l15c0gblN1/f1BTEguKSAscpTjx/+vS9q8yBBoAK2MOjR4EUKFAXzcuG0paxsTE7duxgzpw5zJkzh/v37wNgampKp06dGD58OAULFkzz+wohPj8J0IUQQmQac+bMoX///knOq9Vqdu7cyZUrVzh16hT29vaf3PbPh35mwt8TtMcGwQbY37Ln+bGXKOPieM67wXlBihTpQIsWrri56TFixAgePIjm7t27zJ8/XycnPC0ZGRnx448/MmDAAB4/fkxcXBx58+bFLC3yaIQQXwzZB10IIUSm8OTJEwYMGKA9rl+/PosWLWLcuHHY2dkB8OjRIwYPHvzBNlRqFdeCrjH33Fw6bO7AoQeHtGW1C9TGRM8E91h3XHeVJMEvgUf7H6GMi3unhYpAfS5e3MvVq2OoVCkbrVq14q+//tLWWLRoUVoN+YMUCgWOjo64uLhIcC7EV0hW0IUQQmQKixYtIiEhAYB+/foxe/ZsbVmvXr1wdXUlNDSUjRs3MmPGDGxsbEhQJXDh+QWOPzzOsUfH+PvR34TEhGivc7R0pHaB2kRERHBl+xVyLMjLyacn37tzNooW7cytW0eBM1SpUoVSpZxRKv95OrRYsWKULVsWf39/7t+/j1KpxNDQMD2nQwjxFZMAXQghRKbw999/az8PGTJEp8zOzo7vvvsO37m+KI2VnDt3jsaNG3Mv5B4VF1fUqWtmaIa7gzvVHKtRQq8EPXv6sGrVMuLi3ujUMzIqQLNm/Zk+vTs5cxprV6pDQ0NRq9U6ddVqNSEhmsBfT08PfX39NBu3ECLrkQBdCCFEpvB29RzA0tISgIi4CE48OsGxh8fYkn0LDAduol3dLpKzCEVzFaVwzsJUc6xG9fzVcbNx49CBw4wb6suYM2OS3Cdv3joMGuSDj09jnUC7QoUKnD17lhs3brBjxw4aNmyoLduwYQMPHjwAoGrVqujpSQapECLlJEAXQgiRKbi6umq3Fpy5bCavCr9iycUlxCX+P0dcAegDOTR1QZOrfcPrBgqFgsjISObNW0mTqV149eq2TtsKhSnVqnVh8uT+VKyY/BuF+vXrx9mzZwFo2bIlnTp1Ilu2bGzcuJF169bp1BNCiNSQAF0IIUSm0LNnT+bPnw/ALwG/oI7QpJnkMckDgfD89HN4CNW/qU7hwoW11927d5+RI+fw559LUSojdNo0N89P9+79GTOmOzly5PjX+3fq1Ilt27axZcsWEhMTWblyZZI6HTp0kBcFCSFSTX4HJ4QQ4ot39eVVSriVoFu3bgCoT6ohAFgOz4c95/n853AJTGJMmDJ5Cmq1ms2b91O8eFMKFy7Mxo0zdYLzIkVqsWbNVsLC7jNr1k//GZwD6Ovrs379eoYPH65NsXnL2tqaMWPGsGrVKklvEUKkmqygCyGE+GKdfXqW347/xvbb21nUdBELFizA0NCQhQsXwgXdujY2NixevIQ//vCnXr2uhIff1CnX1zehadPvGDu2P7GxMaxZs4ZNm1ZiZWVF06ZN+fbbbzEw+Pd/Fg0NDZkwYQIjRoxg9+7dHD16lFq1atGwYUPZ7lAIkWYkQBdCCPFFUavVHHt4jN+O/8b+gP0AKFBw+/VtDA0NWbBgAYMHD2b58uXcu3cPU1NTChYszYEDD2jevDMqVbhOe9mzO/DDD/3o3/979PX1ad++PXv37tWps3z5cgoWLMjWrVv55ptv/rOP5ubmNG/eHCMjIxo1aiRbKgoh0pQE6EIIIT6JWq1m7969zJ07l1OnTpGYmIibmxu9evWiTZs2/7kK/W/23NvD+GPjOfH4BAD6Cn06f9OZYVWHUTRXUW09Z2dnfvnlV/z8DjF1qi9PngwAdLc+LF26OiNG+NC8eTMMDAxISEigVq1aOts1visgIIA6depw7tw5nJycUjwGIYRILUmUE0II8dESEhLw9PSkYcOG7Nixg9evXxMaGsqRI0fo2LEj9erVIzIyMsXtzzg9gxOPT2Ckb0Sfsn24632X5c2X6wTnT55E0b79AszMSjJgQF2ePNnO2+DcwMCYzp27c/HiRS5cOErr1q20PzBs3LhRG5znypWLxYsX8/DhQ3bt2kXp0qUBeP36NePHj09x/4UQIi3ICroQQoiPNnr0aFatWqU9zpkzJ0ZGRjx//hyAw4cP061bNzZt2vSfbT2JeMKee3to7NKYPBZ5ABhVfRQlcpdgkPsg7C3stXXVati6NZDRo+dw/fpiIEynrdy58zJgQD969epJrly5kr3f4sWLtZ/XrFlDvXr1AHB0dKRixYoUKFCAiIgI1q5dy6xZs8iWLdtHzYkQQqQ1WUEXQgjxUcLDw5k1axYABgYGLFu2jBcvXvD06VN2796NlZUVAJs3b+bmzZtJrg+ODmbzjc14/eVFkdlFcJjhQM8dPZl+arq2TlXHqkyrP00bnIeFqRkw4DDW1i1p1aoQ169P5d3gvHLlqmzYsIGnTx8wYsTwDwbnADdu3AA0D5N6eHjolOXIkYNGjRoBEBMTw8OHDz99goQQIo3ICroQQoiPsm3bNqKjowH4/vvv6dq1q7asQYMGjB49mkGDBgGaFeq3qSIv37yk4ZqGXHpxCfU7eeJ6Cj3K5ilLPst8OvdRq+H48WhGjlzLiRO+qNVXdcoNDY3o1Kkj3t7elClT5qP7//ZBzujoaOLi4jAxMdEpDw0NTVJXCCEyggToQgghPsqzZ8+0n+vUqZOkvHqt6uAIFIA9b/YwHk2Anjtbbh5HPEaNGtfcrtQpUIc6BepQw6kG1ibW2usjI8HP7xGzZs0lKGgREKLTfp489vTr50XPnj2xsbH55P5Xq1aNtWvX8ubNG+bOncvAgQO1ZRcuXGD/fs2OMfb29hQoUOCT2xdCiLQiAboQQoiPYm1trf189epVWrduzb2Qe/x5608OPjjI4fuHobum/LbqNmq1GoVCgZ5Cjy1tt+Ccw1mba/6u8+fVjBt3nN27fUlM3AqodMrd3d3x8fGhZcuWqVrZ7tevH2vXrgVg0KBBnD59Gg8PD65fv87ixYtRqTT37dOnT6p2ohFCiNSS70BCCCE+SuPGjdHT00OlUuHr68utQrfYFLgJlfqdgDoKeAC9W/UmUZ2IgULzz0y1/NV02oqKgpUrY5g8eR2Bgb7AZZ1yIyMj2rdvj7e3N+XKlUuT/ru7uzNw4ECmT9fkvG/cuJGNGzfq1KlUqZI2TUcIITKKPCQqhBDiozg4ONC2bVsAwsLC2LBqAyq1ilwRudA/oA/zgKlQ9kFZprSbgoFe0jWgq1fB0/MxOXKMwMvLgcDAHrwbnNvZ2TFu3DgePXrEihUr0iw4f2vq1KlMnz6d3Llz65w3NjamZ8+e7N+/X94IKoTIcLKCLoQQ4j89Dn/Mb8d/o/PIzty9exd/f384AdyA189ea+s5OjqyceNGFAqF9lxMDGzcqGbKlBNcu+YLbAESddovX748AwYMoHXr1hgZGaXbOBQKBT/++CNeXl7s37+fJ0+eYGVlhYeHx7/uACOEEJ+TBOhCCCE+6FnkM34//jsLLywkPjGe66+uc+TIEWbMmMH8+fO1D45aW1vTrVs3hg0bpn2A8/ZtmDMnliVL1hMd7Qtc/OB9bt++zdmzZ2nQoAE5cuRI93EZGxvTpEmTdL+PEEKkhAToQgghknj55iWTTkxi3vl5xCbEAlDTqSa/1PwFc3NzRo0axYgRI3j8+DGJiYk4ODhgZGREfDz88QfMmvWUU6fmAwuAVzptKxQK1Gq1zrmIiAhmzZrFnj17OHbsWIp2aRFCiK+FBOhCCJEFHTx4EF9fXw4ePEhMTAzOzs706NGD3r17s+zmMkYeGkm0UrPneRWHKvxa61dqFail04a+vj5OTk4ABATAggVqFi06TWioL7AJSNCpX65cOZ49e6az6t68eXNiYmL4888/iYuL4/bt2/Ts2ZNt27al9xQIIcQXSwJ0IYTIQtRqNT/99JN2J5O37ty5w9ChQ1mwYAF95/clWhlNhbwV+LXWr3gU9NDJKX8rIQF27oS5c+PYv38D4Auc16ljYGBA69at+eGHHwgLC6Nhw4YAlChRgqNHj2rTWQICAqhUqRKvXr1ix44d3L9/n0KFCqXLHAghxJdOdnERQogsZP78+TrBea58ubBsZglumuOAgACWDFjCX+3/4nSP09QrVC9JcP70KYwdC/nyPadFizHs3+8IdOHd4Dx37tz8/PPPBAYGsm7dOipVqsTu3bu15aNHj9bJNS9YsCA+Pj6A5oeIPXv2pPnYhRAis5AVdCGEyCISExOZOHGi5iA7VB9SnQuqC7xRvsHW3RbLeEvu3rzLrRu3iL4ajaLIP4G5SgUHDsC8ebB9+xlUKl9gA++nsZQuXZoffviBdu3aYWJiolMWGRmp/Vy4cOEk/StSpEiydYUQIquRAF0IIbKIU6dO8YhH0A4oCsfijgHgaOLIxAYTye6WnYYNNCko69ato3Xr1rx+DcuWwfz58QQEbESTxnJWp119fX1atWqFj48P7u7uyabDgGYLxrd27dqFm5ubTvlff/2VbF0hhMhqJEAXQogsYvrl6dD9n+MGzg3wLudN/M14GhdrjKrIP28EvXfPls6dYcOGlyiV84H5wAud9nLmzEnv3r3p27cv+fLl+8/7d+7cmXHjxgEwfvx4HB0dadeuHUqlknnz5rFy5UoALC0tadasWarHK4QQmZUE6EII8ZUKiQlBmajE1twWgLoOddn6fCtcBg9LD3aP2Y1SqWTXrV0AHD16EegL9OHKlTiuXOkCrAeUOu26ubnxww8/0L59e0xNTT+6P87Oznh6erJixQqio6Pp3LkzvXr1IjExkbi4OG29oUOHki1btlSOXgghMq9Pekj0999/p3z58lhYWGBjY0Pz5s25ffu2Th21Ws3YsWOxt7fH1NSUmjVrcv369TTttBBCiA+7/fo2fXf2Jd/0fPxy9Bft+e8bfE+ulblgJxxYd4DNmzejVqsJCLCkW7d4GjQoBlQH+gAVgFW8Dc719PRo3bo1x44d4+LFi3Tr1u2TgvO35s+fT/PmzbXH0dHROsH5Dz/8wPDhw1M0biGE+Fp80gr60aNH6devH+XLlychIYGRI0dSr149bty4oV3tmDx5MtOnT2f58uUULlyY8ePH4+Hhwe3bt7GwsEiXQQghRFanVqs5+OAgM07PYNfdXdrzl19eRqVWoafQw8jIiIF9BzJixAjUaiNat96GqakzMTHFgRnAPOCZTrs5cuSgV69e9O3bN03ywk1MTNiyZQv79u1j4cKFXL58GX19fSpXrkzfvn2pWLFiqu8hhBCZ3ScF6O9ve7Vs2TJsbGzw9/enevXqqNVqZs6cyciRI2nZsiUAK1aswNbWlrVr19K7d++067kQQmRh4eHhrFq1ih07dhBgGkBQ0SAiTCMAUKCgaZGm/FjpR2rkr6Hz0GarVkNYubIEt25VBh4REzMDWAfE67RfsmRJfvjhBzp27JiilfJ/o1AoqF+/PvXr10/TdoUQ4muRqhz08PBwAO1etg8ePODFixfUq1dPW8fY2JgaNWpw8uTJZAP0uLg4nV9vRkRo/oFRKpUolcok9dPb23tmxL0zO5m71JH5S7mMmru4uDj27t3LkydPMDc3x8PDgzx58qT7fY8dO0bbtm0JCQnRnKgDmALxkOtJLjYM2kDVYlUBSEhIIDERdu9WsGCBHnv3JgIxQHPghE67CoWCevXq8dNPP1G9enVtYC9fk8mTv7OpI/OXcjJ3KZfRc/ex91Wo1Wp1Sm6gVqtp1qwZoaGhHD9+HICTJ09SpUoVnj59ir29vbZur169ePjwIXv37k3SztixY7VP9b9r7dq1mJmZpaRrQgiRrtRqNTt27GDz5s3ahQrQbDdYtWpVevbsibm5+Ue1FRISQkREBJaWljov7klOojqR3fd3s/TKUlSnVHD3/wUWwDeAPxCr2aJwypQpxMRYsn+/I/v2OfHqVRSwCJgLPNVp18zMDA8PDxo1aoStre1HzoIQQohPFR0dTceOHQkPD8fS0vKD9VK8gt6/f3+uXLnC33//naTs/T1w1Wr1B/fFHT58OAMHDtQeR0RE4ODgQL169f614+lFqVSyf/9+PDw8MDQ0/Oz3z8xk7lJH5i/lPvfcjRgxgqVLlyY5n5iYyNGjRwkNDeXQoUP/+j1s9+7dTJ06VbvAAVC5cmUGDRrEt99+q1P3aeRTllxcwtJLS3n25hkUBBKgjmMdJk2ahKurKwcOHMDHx4fAwEAePXJk6tQyXLpUCKXyMtAfWAvE6bTr6upK3759yZ07N02bNpWvu08kf2dTR+Yv5WTuUi6j5+5tpsh/SVGA7u3tzfbt2zl27JjO3rd2dnYAvHjxQufXvEFBQR9clTE2NsbY2DjJeUNDwwz9osvo+2dmMnepI/OXcp9j7s6fP8/UqVO1x23atKFhw4bcvn2b+fPnEx4ezpUrV5gyZco/b+18z7Rp0/jpp5+SnD916hStW7dm/PjxjBgxggMBB5h3fh7bb28nUZ2oqRQFXITsAdnZdmWb9gH9mjWb0qZNCaZMeQMU49y5P9Fsen5c5x4KhYJvv/0WHx8fatWqRUJCArt27ZKvu1SQuUsdmb+Uk7lLuYyau4+95ydts6hWq+nfvz9btmzh0KFDFChQQKe8QIEC2NnZsX//fu25+Ph4jh49iru7+6fcSgghvkhz587Vfv7999/ZsGED3bp1Y+LEiZw6dUr7zXfx4sU6z9e8deLECZ3gvEiRInTr1g1XV1ftuZ9//pmDBw8y5MAQtt7aSqI6kWqO1ZhUYRJMBw5AY/fGZMuWjWvXwMsL7O1hyhRLYBdQAGjDu8G5lZUVgwYN4t69e/z555/Url37g7/ZFEIIkbE+aQW9X79+rF27lm3btmFhYcGLF5q3yllZWWFqaopCoWDAgAFMmDABFxcXXFxcmDBhAmZmZnTs2DFdBiCEEJ/T27Q+Y2NjfHx8dMqKFStGkyZN2Lp1K8HBwdy+fZtvvvlGp87MmTO1n0eMGMH48eMBOPX4FN7LvLnw+wWIg1mzZjFw/EDOPj1Ln3J9KG5TnICAAIYmDgUM8PcvRI0acOwYwBXAD4ViNWp1bJI++fj40Llz54/OixdCCJGxPilAnzdvHgA1a9bUOb9s2TK6du0KwJAhQ4iJicHLy4vQ0FAqVqzIvn37ZA90IcRXISEhAQAjIyNMTEySlFtZWWk/v/+0/tuHSwFy587NyFEjWX1lNdNOTePyy8ua66tZEX4gnN27d7Nlyxa+c/tOe72xsRPZs88kNLQ1N2/acvPmVsAXOPL/9v+5l6OjI0uWLKFOnTqyUi6EEJnMJwXoH7Phi0KhYOzYsYwdOzalfRJCiM/iwoULLFmyhDt37mBsbEzNmjXp1q0bOXPm/OA1rq6uPHjwgMjISLZt20aLFi20ZeHh4Wzbtg3QBPCFChXSuTY+Pl6T9qIPFjUtKLmwJAGhAQCYGJjQvkR7rvtf5xznSExMJDo6GktLK44fhzlzYMsWPRISvgOWoAnMn3ywn9u2baNUqVIpnRohhBAZKFX7oAshRGYUFxdH9+7dWbt2rc75v/76izFjxrBkyRLat2+f7LU9e/bkr7/+AqBbt248efKERo0acevWLcaMGUNoaCgAbdu2xdraWudaY2NjcuTJQUj7EAKsAiAUcpvl5sdKP9KnXB8UcQryddI8eG9ubsfatRbMmwdXrwJcA/zQ01uFShXzr+ObPHmyBOdCCJGJfdJDokII8TVILjh/Kzo6mk6dOiV5c/JbTZs2xcPDA9CsmPv4+ODs7EyTJk3w9/cHNC9ve/e3iPGJ/7yls0u7LpptyCPA5b4Lx1oeY3i14UQFR9GxY0eiovICM4mPD8DLS83Vq9vQ06sDlAQW6gTn7+8G4Orqyrp16xg8ePAnz4kQQogvhwToQogs5cKFC9rg3MzMDD8/P4KCgrh+/bp21VylUjF06NBk0/r09PTYsmULLVu2TLb9AgUKcPDgQQoVKkRwdDBjDo8h7/S82lSWAQMGYH7MHGbB3VV3cXVxJV8+JxwcvNm9+0fgNuBJfPxcDAycgeaoVIe07VtYWODj48OdO3eIjIzkyJEjbN++HX9/f65du/bBlX8hhBCZh6S4CCGylHdfMDRx4kT69+8PaB7aXLNmDXfv3sXf358rV67g7+9PuXLlkrRhbm7O5s2buXz5MqtWreLx48dYWFjQqFEjvv32W17HvmbI/iHMPTeXKGWU5r4XlzK+9njy58/P7o27adq0KWFh+qjV3/P0aV8gP3AD6Iue3kpUqmj+/zwqAC4uLnh7e+Pp6anzAqQaNWqkxzQJIYTIQBKgCyGylLt372o/t2vXTqdMT0+PNm3aaFNV7ty5k2yA/pabmxtubm7a40fhj/hx348svriY2ATNdodutm6MrDaSlsX+WXE3Na1KgwbP2LTJkIQEPTR7l3fl7W4sKtU/92jQoAE+Pj7Ur18fPT35pacQQmQFEqALIbKUd99c/PLlS2xsbHTKX758qf2c3DaKHxKfGE/ZhWV5Hf0agEr5KvFztZ9p5NIIhUJBfDxs2Ax+fnDqFEA8sABj49nExd3Xacvc3JyuXbvSv39/ihQp8sljFEIIkblJgC6EyFJq1aql3Yv8119/Zf369dqV6UePHrFs2TJA8wBmlSpV/rUtZaISQ33Ng5pG+kb0KtOL009PM7LaSGo51UKhUPD8OSxYoPmjebfbLfT0ZqOnt5yEhCjefdlooUKF8Pb2pmvXrjr7qQshhMhaJEAXQmQpXbt2ZdSoUURFRbFx40bu3r1L27ZtCQoKYvny5YSFhQGabRJtbW0/2M6++/vo+1dfln67lBpOmjzwX2r9gr6ePmq1ZpXczw82bYKEBBWwB2NjX+Li9qJS6aaxeHh44OPjQ8OGDdHX10/H0QshhMgMJEAXQmQp2bNnZ9myZbRv3x6VSsWlS5e4dOmSTh1nZ2emT5+e7PWvo1/z494fWX1lNQDjj4/XBujxcfqsX68JzC9eBIgAlmNi4kds7D2d1XIzMzM8PT3p378/rq6uaT9QIYQQmZYE6EKILKdNmzZYW1szdOhQLmoiaUCT1tKuXTumTZuWJDddrVaz+spqftz7I8ExwShQ4F3Bm/G1x/PwIcybB4sXQ3AwwB309Wejp7cMpfINsbH/tFOgQAH69+9P9+7dk7zISAghhAAJ0IUQWZSHhwd169bl0qVL3LlzB2NjY9zd3ZME5gABoQH02dmH/QH7AShpU5JFTRcTe78CXTvCn39q9k6HfZiY+BIbu5vEREhM/KeNOnXq4OPjQ+PGjSWNRQghxL+SAF0IkWUpFApKly5N6dKl/7Xeqcen2B+wH2N9Y0ZUGYPt/Z/o1diQK1cAIoGVmJn5ER19W2e13NTUlC5dutC/f39KlCiRnkMRQgjxFZEAXQghkhEVH0U2o2wAdCzZkTMBN4k768ms1i6EhADcw8BgDnp6S4mPjyA6+p9r8+fPr01jyZEjR4b0XwghROYlAboQQrwjWhnNmMNjWHdtHVf6XOW6f3Z8fRVs3TqexEQ1sB9TU19iY/8iIUGtc22tWrXw8fGhadOmksYihBAixSRAF0KI/9t3fx99dvbhQdgDAEp13MTjbT2BN8Cq/6ex3CQm5p9rTExM+O677/D29qZkyZIZ0m8hhBBfFwnQhRBZ3quoVwzcN1C7daJepAOq7fN4fLcY+vqD0NdfQnx8uE4ai4ODA/369eP7778nZ86cGdRzIYQQXyMJ0IUQWdrG65vota0vYcrXoFbAaW9UBz0wMVhInGIHiYlqnd1Yqlevjo+PD82aNcPAQL6FCiGESHvyr4sQIkuKj4eNG8HnyJ+E5XsNT4rDpiaYxe8kOsGX2IR/6hobG9OpUye8vb0pVapUhvVZCCFE1iABuhAiS3n1CubOV7JgniHPnwNGg1HYPsTw5TXi4yfxThYLefPmpV+/fvTs2ZNcuXJlVJeFEEJkMRKgCyGyhCtXYIpvBGuDB6IyfgXPB2Bs7Ed8/DbUj1XEv1O3atWq+Pj40Lx5cwwNDTOsz0IIIbImCdCFEF+txET46y+YORMOPzgMjT0h8TEcBthOXNw/dY2MjOjYsSPe3t6UKVMmg3oshBBCSIAuhPgKRUTAsmXg6wsBj6PBvT/kXQZLgRjduvb29nh5edGzZ09sbGwypL9CCCHEuyRAF0J8Ne7fh/nzYelSiIxUQ+55kH8oHHsDuu8Uwt3dHR8fH1q2bClpLEIIIb4oEqALITI1tRqOHFEwYUIFzp0zQK2OAdZhbDyLuFdX4NU/dQ0NDWnfvj3e3t6UL18+w/oshBBC/BsJ0IUQmVJMjIrBgy+wYkV23rwpBCQAI9HXX0BiYohOfrmtrS1eXl706tULOzu7jOqyEEII8VEkQBdCZCpBQeDnp2Ty5Eji48sCJ4AhwJ+ASuelQhUrVsTHx4fWrVtjZGSUIf0VQgghPpUE6EKITOHqVc1uLGvWQFxcIrADmAZc1a2op/nToU0H1q5d+9n7KYQQQqSWBOhCiC+WSgW7d8OMGXDwIMBTYD4wBwjVrZwNDMoboHqlQnVdxZYtWwgODiZnzpyfvd9CCCFEauhldAeEEOJ9UVEwbx64ukKTJmoOHjwFdEChcALGoxOc2wMtoNyYctzbfA8fDx8A4uLi2Lx58+fvvBBCCJFKsoIuhPhiPHkCs2fDwoUQGhoHbEBPzxeV6jyg2bFFqzhYVrPEq5UXXb/pyq1Tt7C3sKdOnTrMnDkTgGfPnn32MQghhBCpJQG6ECLDnTgRz8yZemzdqk9i4gtgPvr680lMDEKl+qde7ty5KVy4MCdOnIBwmFx2Mr3r9kapVHKLWwBcu3ZNW9/Kyuozj0QIIYRIPQnQhcjC1Go1J06c4M8//yQsLAx7e3s6dOhAsWLF0v3ecXEJDBx4jJUrc/DmTSngDOALbAASdHZjwQ6sa1pzbf41Htx6QKVKleAJ/D7+dxrWa0iePHkAuHXrFtOnT9de1rRp03QfhxBCCJHWJEAXIot6+PAhbdu25ezZszrnf/31V1q3bs3SpUuxsLBI8/tGRMDChQmMHv2amJiqwEagF3BOt6ICcIVKrSoxtP1QmhRpgoGeAbkr5Mbd3Z2TJ0/y8OFDChcujIeHB8+ePePKlSskJCQA8O233+Ls7Jzm/RdCCCHSmwToQmRBr1+/pmbNmgQGBiZbvmnTJoKDg9m3bx8GBmnzbeLhQ/Dzg0WLICIiGFiAZjeWV7oVTYGSYJfXjtNLT5PfOr9OsUKhYN26ddSsWZMHDx4QFxfHzp07deqUKFGCJUuWpEm/hRBCiM9NdnERIguaOHGiNjgvUKAAy5cv5+LFi0ybNk2bt3348GE2bNiQ6nudPg3t2kGhQjBt2jkiIroA+YCxvBucu7m5MeaXMeR0ywnn4cXWFzy6+ijZNh0dHTl79iwDBw4ke/bs2vM2NjaMHDmSEydOkCtXrlT3XQghhMgIsoIuRBajVCpZunQpAEZGRhw5cgRHR0cASpUqhaurKw0bNgRg4cKFdOzY8ZPvkZAAW7dq9i8/dUoJbAbFdJJLY7Etb8vGqRupWrUqCoWCQk6F6HK6CwAbNmygWrVqyd4jV65cTJs2jd9//5179+5x7NgxPD09MTU1/eT+CiGEEF8SCdCFyGKePn1KaKhmH/F69eppg/O36tevT968eXn69CmXL1/+pLbDw2HJEvD1hYcPg4CFwDzgGby7RaIp4Ah9u/Zl9tDZ6Cn++WVepUqVtJ+Dg4P/855GRka4uLhw9+7dNEvHEUIIITKS/GsmRBajp/dPMBwbG5ukXKVSERcXl6TuvwkMhFmzNMF5ZOQF0J8CbAHideoZ2xtTumZpTm89DbdB8VihE5wDnDp1SvtZ0lSEEEJkRZKDLkQWkzdvXvLmzQvAoUOHuHLlik75unXreP36NaC7mp2c06ehTRsoWFDJzJnriVQWB8pC4nreBud6enrUaVyHORvmEP04mt1zdmOmMANg0aJF7NixA/X/30B07do1Ro4cqW2/bdu2aTFkIYQQIlORFXQhshh9fX169+7N6NGjUalU1KhRAx8fH9zc3Dh48CALFy7U1vXy8kpyfWKiJr98+nQ4deoVmI0Ho2UQFwnvLMibWpjSv09/vLy8cHJy0p63tramT58+TJ8+HaVSybfffkuRIkUwNzfH399fW8/d3Z0qVaqkyxwIIYQQXzIJ0IXIggYOHMi2bdvw9/cnLCyMX375JUmdDh060KhRI+1xZCQsXapJZXnw4BIY/Qb6myFarXuhOeTKnYsTe05QuHDhZO//9sHO7du3A3D79m2dcldXVzZt2oRCoUjdQIUQQohMSFJchMiCsmXLxoEDB2jXrl2SPHNTU1OGDBnCypUrUSgUPH4MQ4aAfaEgBoybzIMHNYDSEL8JEv8Jzg1yGGi+o7yB1w9e06ZNG5RKZbL3NzIyYsuWLaxcuZKKFStqzzs7OzNp0iROnz6tfTuoEEIIkdXICroQWZS1tTXr169n8uTJ7Ny5k7CwMPLkyUOLFi2wtrbm/HmYPCOGjRfXgtE0iLsJEe81ooBSZUuxYskKvvnmG06fPk3Hjh158OABV65cYfv27bRq1SrZ++vr6/Pdd9/x3XffkZCQQGJiIsbGxuk/cCGEEOILJwG6EFmco6OjNtdcpYI/tycwZsU+roXPhpA9cFcJCclfW7ZMWc6dPadNRalUqRLz5s2jQYMGAKxcufKDAfq7DAwMZItEIYQQ4v/kX0QhBFFRsGIFTJ+eyH3L5hD6FwTq1lEoFDRu3JjKlStrd1pp2LBhkjxxDw8P7eenT5+mc8+FEEKIr48E6EJkYc+fw/jZgaxerCYiaBMwB3ioU8fS0pLu3bvTr18/nJ2dOXHihLbs5s2bSdp894FPS0vL9Oq6EEII8dWSAF2ILOjKFZg2XcWqSyNRK6ZCsBpI1KlTpEgRvL296dKlCxYWFtrz5cuXx8bGhqCgILZu3cr+/fu1q+YxMTEMGjRIW7dp06afZTxCCCHE10QCdCGyCLUa9u2DqVMTOXBmAZiPgOfhSeo1atQIHx8fPDw8kn2TqJGREf3799fuo16vXj1q1qyJo6Mje/bsISgoCNA8hNq1a9f0HpYQQgjx1ZEAXYivXFwcrFkDU6aEcev2IjD6HeJCIfKfOhYWFnTr1o3+/fvj4uLyn20OGzaMc+fOsWPHDgCOHDmiU25qasrGjRvJnj17Wg5FCCGEyBJkH3QhMrHAwEAGDRpE3rx5MTAwwMbGhj59+nDjxg2Cg2H8eMib9wY9enhx65Y9qIdogvP/K1CoAL6+vjx58oRZs2Z9VHAOYGhoyJYtW5gxYwaFChXSnjcwMKBt27acPn2aunXrpvl4hRBCiKxAVtCFyKQOHDhA8+bNiYqK0p579eoVCxYcYuFCN/T175KQMAfYn+Taku4lmThyIg0aNEg2jeVjGBgYMGDAAHx8fAgICCAmJgYHBwesra1TOCIhhBBCgAToQmRKgYGBOsG5oaERjo6dePCgPirVM9TqaSQk3Ne5xtzcnHqt6vGjz49ULVM1zfqip6eHs7NzmrUnhBBCZHUSoAuRCfn6+v4/ONendOkJxMQ05NatBUAPIEqnrq2DLcMHDadr165YWVllRHeFEEII8QkkQBciE1qzZgcwAHDj4sX1wNCklQoCFaF1+9b88O0Pn7V/QgghhEg5CdCFyEQeP4YpUyIICvoeWAzM1Ck3MDYgoWQCVACMgR0wctrIz99RIYQQQqSYBOhCZAIXLsCYMXf466/ZqNXLgDc65XYOdkSXjiaiWASYQrYb2YjaFoWeUk/SWoQQ4gOCgoKIi4vL6G58MpVKhYODA8+ePUvxg/5Z1eeYu9y5c2NiYpKqNiRAF+ILpVLBzp0qfv55H1ev+gK7k61Xt25dhs4Zisc6D5yzO1PhRQXWblgLQMPGDTEzM/uMvRZCiMwhIiIChUKBg4NDRnflk6lUKqysrLC0tJQA/ROl99wlJiby9OlTbGxsUhWkf3LPjh07RtOmTbG3t0ehUPDnn3/qlKvVasaOHYu9vT2mpqbUrFmT69evp7iDQmQ1MTHg6xuJvf0cmjVz5erVhrwbnJuYmlC4dmGoqDk+cOAAnap1okxAGWJmxLD297XaugMHDvzMvRdCiMwhPDycXLlyZXQ3xFdGX1+fvHnz8urVq1S188kBelRUFG5ubsyePTvZ8smTJzN9+nRmz57NuXPnsLOzw8PDg8jIyGTrCyE0Xr2CRYtMsLMbzA8/5OPly/7AbW25vYM95buWJ+GHBO5Uv4NxI2P0smn+CgcFBXFh5QWeBj7V1p82bRq1a9f+3MMQQohMQ6FQZHQXxFdIX18/1W18copLw4YNadiwYbJlarWamTNnMnLkSFq2bAnAihUrsLW1Ze3atfTu3Tt1vRXiK3Trlhpv710cOjQPlWoXoNYpL+teFv3K+pzNdpZnes8AqOpYlaFVhpK7QW6mTZ3G1q1bSUhIQKFQ0LBhQwYNGiTBuRBCCJFJpWkO+oMHD3jx4gX16tXTnjM2NqZGjRqcPHky2QA9Li5O5wGNiIgIAJRKJUqlMi2791He3jMj7p3ZZda5u3jxIosWLeLixYsAlClThu+//57SpUun2z3Vati3L4oBAxZz//5S4KZOuYGBIV26fEfuWrmZdH+S9nwTlyYMrjyYyvkqa8+tWbOGmJgYQkNDsbKyIlu2bEDm+/+QGpn1a+9LIHOXcjJ3qZPR86dSqVCpVBly79RSq9Xa/2bWMWSUzzV3KpUq2a/tj/16T9MA/cWLFwDY2trqnLe1teXhw4fJXvP7778zbty4JOf37duXoQ+37d+f9PXo4uNklrlTqVQsXryYXbt26Zz39/dn0aJFNGnShO7du6fpQySJiQp27VKxefN+wsLWAOFJKxlCglLJrVu3qFSvEiZ6Jrhbu9PCpgUOJg6EXgll15VdSa8TmeZr70skc5dyMnepk1Hz5+DgkOl3uZL04ZRL77kLDg7m0qVLSc5HR0d/1PXpsovL+zldarX6g3lew4cP13mQLSIiAgcHB+rVq4elpWV6dO9fKZVK9u/fj4eHB4aGhp/9/plZZpu70aNHJwnO37Vz507c3NwYM2ZMqu8VHq5m5MgjrFo1h5iYHbyfxmJkYoRDTQceFn9IwosEWAMnT56kefPmPPnxCZbGn//vQmaS2b72viQydyknc5c6GT1/z549y5A4Iy2o1WoiIyOxsLCQPPpP9LnmLmfOnJQsWTLJ+beZIv8lTQN0Ozs7QLOSnidPHu35oKCgJKvqbxkbG2NsbJzkvKGhYYZ+w8vo+2dmmWHugoODmTFjBqB5mGPSpEn07t0btVrN/PnzGTZsGCqVimnTpjFo0CCyZ8+eovvcvh2Ft/dqDh70Q6VKZjcjC7BpakN4sXDuJ94HwCq7FeEm4RALs2fPZuDAgWnywElWkBm+9r5UMncpJ3OXOhk1f3p6eplui8KuXbuyYsUKQPNvl729PY0bN6ZevXraZ/8+ZNmyZXTt2pUFCxYwd+5c7t27h6GhIQUKFKB9+/YMHZrMG6m/Qm/TWhQKRbr+/9fT00v26/pjv9bTNEAvUKAAdnZ27N+/X5u/Gx8fz9GjR5k0adJ/XC3E5/PHH39on33w8vJi0KBB2rLBgwcTGBjI3LlziY2N5Y8//qBPnz6f1P5ffwUyePBcbt5cDITqlNnb5yU6exRh1cPAFoIIgkQokbsEVYyrMLnDZNoeb8vevXt59OgRV69epVSpUqkcsRBCiK9BgwYNWLJkCaGhoTx+/Jjvv/+esLAwnj9/rq3zww8/EBERwbJly7TnrKysWLJkCQMHDsTX15caNWoQFxfHlStXuHHjRkYMRfyLTw7Q37x5w71797THDx484NKlS+TIkQNHR0cGDBjAhAkTcHFxwcXFhQkTJmBmZkbHjh3TtONCpEZAQID2c/PmzZOUN2/enLlz5wKar/GPkZioZsqUo0yf7surV9sA3YdPKrlXZuCAH2nevDmOzRzBFoiB/jX6071Ud4rnLM7u3bsxNTSlWLFi7N27F/j4X4cJIYRIGbUaPjI1OM2ZmcGnZFoYGxtjZ2eHmZkZxYoVo127dixfvlybxQBgampKXFyczjmAHTt20LZtW3r06KE9V7x48VSPQaS9Tw7Qz58/T61atbTHb/PHPT09Wb58OUOGDCEmJgYvLy9CQ0OpWLEi+/btw8LCIu16LUQqvfsAcmBgYJLyd8+93RXlQ0JCovnxx7X88YcvcXFXdcr0DQxwqJqPp8We0va7NrSp3AaAIglFePHHC7gD7Zu2p3Se0tonu9VqtTY4B8iXL9+nDk8IIcQniI4Gc/OMufebN/Af/8x8UEBAAHv27PnotAk7OzuOHj3Kw4cPyZ8/f8puKj6LT06+qVmzJmq1Osmf5cuXA5qcnrFjx/L8+XNiY2M5evQoJUqUSOt+C5Eq9evX136ePHkyoaH/pKGEhIQwZcoU7fG724a+6/LlR1SvPoxcuRxYubKnTnBulsMc8wbmJA5IILBmIEpbJaefntaWd+vUTbOzYiJ0796dc+fOAZrfUPn4+HDzpmbbxSpVqlCwYME0GbMQQojMb+fOnVhaWpInTx5cXFy4cePGR+ePjxkzBmtra5ycnChSpAhdu3Zlw4YNslXjFyhddnER4kvn7u5O2bJl8ff35/bt27i4uNC+fXvUajXr168nJCQEgPLly1OxYkXtdWq1mnXrjjNqlC8BAVt5P42F3EB1iHZ9A/qQ0zQnnUp2omuprpSyK6Wt1q5dO37//Xdu377NnTt3qFChAra2tgQHB5OQkABoftgdNWpUOs+EEEIIMzPNSnZG3ftT1KpVizlz5hAUFMQff/zB3bt38fb2/qhr8+TJw6lTp7h27RpHjx7l5MmTeHp6snjxYvbs2ZPpHpr9mkmALrIkhULBmjVrqFatGq9evSI4OJg5c+bo1LG1tWX16tUoFAqio2P49dd1zJ3rS0TE5fda00OzbaIaagJFgbtQVr8sRxYdwdw06e9NTUxM2LNnD/Xr1+fOnTsAvHz5Uluur6/P/PnzdVb6hRBCpA+FIuVpJp9btmzZcHZ2xsbGBnd3d+rUqcO4ceP49ddfP7qNEiVKUKJECfr168fff/9NtWrVOHr0qE4Ks8hY8qOSyLKKFCnC2bNnad++vU7+nqGhIR06dODMmTMYGprSosUIrKwcmDixh25wbo4mIM+uwtDQgLp161L8eXGYDqwH/zX+/DLmlw/e38nJiYsXL7JgwQIqV66Mvb099vb29O/fnxs3bvD999+n19CFEEJ8JcaMGcPUqVN59uxZiq53dXUFICoqKi27JVJJVtBFlubk5MS6det49eoVV69qcshLlizJxYu3ad58MJcubQESdS/KC1REs1L+GJzinTi2/hgODg4A7N27l6ZNm6JUKpk/fz6jRo364EPSZmZm9OrVi169eqFUKtm1axeNGjWSPZWFEEJ8lJo1a1K8eHEmTJjA7Nmz/7Vu3759sbe3p3bt2uTLl4/nz58zfvx4cufOTeXKlT9Tj8XHkBV0IYDcuXPj7u7OlSuPKVmyPvXrV+PSpY1og3M9oCQY9zam+bTmVM1TVbNSvgr8hvtpg3PQPIDq6ekJaF4lfODAgc8+HiGEEFnHwIEDWbRoEY8fP/7XenXr1uX06dO0adOGwoUL06pVK0xMTDh48CA5c+b8TL0VH0NW0EWW9/TpU8aNm8/yVX4oY8N1yiwsbOjj9T0Pi9yjXaV21C9Un2xG2Wi6uinEauqUKVMmSZtly5Zl8eLFANoHToUQQojUeLtj3vu7rnTs2FHnfTNv672vVatWtGrVKr26J9KQBOgiS1Kr1Zw6dZqRI305enQTanWCTrlpPgvm/zaXdu3aYGxsnOT6d1/+8Pfff9O2bVud8uPHj2s/29jYpHHvhRBCCPE1kxQXkaXExcWxbNkqChWqQJUq7hw5sv6f4FwP8lVwZuGfC4l8GEqXLp2TDc4B2rdvr/08ePBgLl26BGhWNZYvX866desAyJEjBx4eHuk6JiGEEEJ8XWQFXWQJz58/Z8aM+cydO5+oqCDdQjMwq5SNJb8upr17++QbeE/t2rWpUKECZ8+e5dGjR5QuXRpXV1fCwsJ0nqQfOHAgJiYmaTkUIYQQQnzlJEAXaUqtVmd0F3ScOXOGCRN82blzAyqVbhqLrX1xItwfUKNxdVa2WUnubLk/ul2FQsHWrVvx8PDgxo0bANr/vtWtWzeGDx+e+kEIIYQQIkuRAF2k2rVr15g1axZbtmwhJCQEOzs7OnTogI+PD05OTp+lD1evXuXYsWPEx8fj4uJCaGgoEyfO5saNs+/V1KdChVZMmuRDjRru3Au5h3MOZxQKxSff097enrNnz7JkyRIWLVrEzZs3MTQ0pEaNGvTv35/GjRunqF0hhBBCZG0SoItUWb16Nd26ddO+nh7gxYsXzJgxg4ULF/Lnn39St27ddLv/rVu36NWr1zsPZSoAIyBOp56hYU5cPIpws+gpxvTxpKZLFQBccrqk6v7ZsmXDx8cHHx8f1Gq1BORCCCGESDV5SFSk2JkzZ+jatas2OM+WLRsFCxbEyMgI0LyVrEWLFjx8+DBd7n/79m2qVKny/+BcH82Xs5p3g/Ns2Yry48+TKDWzIDcqnERtqeZI4JF06Y8E50IIIYRICxKgixSbMmUKiYmaF/n06NGDx48fM336dAIDA2ncuDEAb968+c83m6WEUqmkVatWhIRE/v9MIvB2X1g9oDiQA2WRABabjefcq3NYGVuxofUGJntMTvP+CCGEEEKkFQnQRYrExMSwbds2AGxtbZk7dy7m5uYA5MqVi2XLlmlfV/92y8G0EBQUxPjx47Gzc+D69euAUlump5eDunWHcuNGAG06uUKzEOK/jScyPhJ3B3cu97lMm+Jt0qwvQgghhBDpQQJ0kSIhISHa1JaKFStq01reyp07N8WKFQPg5cuXqb7fhQsX6Nq1K/nyOTBq1ChCQv5p09CwKH37LiIs7DH790+kWLH8VOpYCUoDKnB95crRrkfJb50/1f0QQgghhEhvEqCLFLG2ttbmXF+6dEmb6vJWeHg4d+/eBTQv60kJpVLJhg0bqFKlKmXLlmXFihUolfH/L9UDKgDFmDy5N3Pnfo+FhZn22ibOTeAYsAKKPi+KgZ48Dy2EECJz69q1K82bN9c5t2nTJkxMTJg8WZO+OXbsWBQKRZI/Bw4cSNe+KRQK/vzzz3Rp28nJiZkzZ6ZL218qCdBFimTLlo0GDRoA8OjRI0aNGqVdUY+NjcXb25uYmBgAWrdu/Ultv3r1igkTJpA/fwHatWvHyZMn3im1pnTpwcyZsx04C9xk1epVbLu1jWbrm/HyjWZlffny5XAIeAglS5ZM3WCFEEKIL9DixYvp1KkTs2fPZsiQIdrzxYsX5/nz5zp/qlevnoE9FZ9KAnSRYoMGDdJ+/v333ylcuDDjx4+nQIECrFq1CgBDQ0O8vb0/qr1Lly7RvXt38uVzYOTIkTx//lRbZmBQnObNF/Do0RMuXJhM376NKO5WHErBhYoXaP5Hc7bf3k6HNR0YPHgwkyZNAkBPT4/u3bun3aCFEEJ8taLioz74JzYh9qPrxihjPqpuasyaNQsfHx/Wrl3L999/r1NmYGCAnZ2dzp/3U1HfdfToUSpUqICxsTF58uRh2LBhOtsnJ7eCXapUKcaOHastB2jRogUKhUJ7PHbsWEqVKsWCBQtwcHDAzMyMNm3aEBYWpm2nZs2aDBgwQKft5s2b07VrV235w4cP+fHHH7W/DcgK5Pf+IsXq1KnDtGnTtIH6kydPePLkibbcwMCA1atXU7Ro0Q+2kZCQwLZt2/D19eXYsWPvlSqwsPiWPn18+OWXWpiYaP5ShsWGseD8Al60ewFvM17igPNw+MxhDkcc1rYwbNgwHB0d02K4QgghvnLmv5t/sKyRSyP+6viX9thmqg3Ryuhk69bIX4MjXY9oj51mOfE6+nWSeuoxKXv79vDhw5k7dy7bt2+nXr16KWrjradPn9KoUSO6du3KypUruXXrFj179sTExEQbgP+Xc+fOYWNjw7Jly2jQoAH6+vrasnv37rFhwwZ27NhBREQEPXr0oF+/fqxZs+aj2t6yZQtubm706tWLnj17pmSImZIE6CJVBg4cSOnSpZk2bRq7d+9GpVJhaGhI69at+emnnyhTpkyy1wUHB7N48WLmzJnD48eP3yu1In/+7xk3zosuXQry7g/LiapE3Oa78Sj8EQA5DHMQeySW6GPROu8mMjAwYNiwYYwbNy6NRyyEEEJknN27d7Nt2za2bdv2wRcBXr16VbuzGoCrqytnz77/Zm2NuXPn4uDgwOzZs1EoFBQtWpRnz54xdOhQRo8ejZ7efydb5M6dG9A8n2ZnZ6dTFhsby4oVK8iXLx8Afn5+NG7cmGnTpiWpm5wcOXKgr6+PhYXFR9X/WkiALlKtVq1a1KpVi4iICLZs2ULr1q11vjG868qVK/j5+bF69WpiY2PfKy1GpUo+zJjRmUqV/rn+5qubFM1VFIVCgb6ePp1KdmL77e385P4THUt2JPHHRDZs2MDx48dRKpUUK1YMT09P8uTJk46jFkII8bV5M/zNB8v09fR1joN+CvpgXT2FblAb+ENgqvr1rm+++YbXr18zYcIEatSogZWVVZI6RYoUYfv27dpjY2PjD7Z38+ZNKleurJM6UqVKFd68ecOTJ09S/VtoR0dHbXAOULlyZVQqFbdv385SAfenkgBdpBlTU1PMrMySfCNITExk+/bt+Pr6cuTIkfeuUmBo2JhWrX5g6tQ65M2r+QahVqs59OAQU05OYe/9vezrvA+PQh4AjK4xmt9q//bPNxNT8PT0xNPTM51HKIQQ4muWzShbhtf9L3nz5mXjxo3UqlWLRo0asWfPHiwsLHTqGBkZ4ezs/FHtqdXqJHndarUm9ebteT09Pe25t5RKJSnxts30aPtrIg+JijSRqErEZ48P31//50GVkJAQaveqjVUeK1q2bKkbnCuyYZGzB6NH3yEkZAfr1tUlb14FCaoE1l9bT7lF5ai7qi577+9FT6GH/3N/7aUmBiZZ5iERIYQQ4n2Ojo7s3LmToKAg6tWrR0RERIrbcnV15eTJkzpB8smTJ7GwsCBv3ryAJoXl+fPn2vKIiAgePHig046hoWGSLZdBs9Pbs2fPtMenTp1CT0+PwoULJ9t2YmIi165d02nDyMgo2ba/ZhKgi1SLTYil7aa2zL8wHz2FHlevXaV3797ky5ePw4sOE/XqnSfVcwKNgGFR6A/ezLhxzrzNhvlp3084+zrTYXMHLjy/gKmBKf3K9+Ou912GVR2WEUMTQgghvkh58+bl0KFDBAcHU69ePcLDw1PUjpeXF48fP8bb25tbt26xbds2xowZw8CBA7X557Vr12bVqlUcP36ca9eu4enpqfMgKGh2cjl48CAvXrwgNDRUe97ExARPT08uX77M8ePH8fHxoW3bttr0ltq1a/PXX3/x119/cevWLby8vHR2eXnb9rFjx3j69CmvXyd92PZrJCkuIlUi4iJotr4ZRwKOYHDPAKuLVpT9uWzSirkKYlO1AAVqGxBvFERQVBDZTbPrVDn44CAPwx+SyywX3hW88SrvRS6zXJ9pJEIIIUTmkjdvXo4ePUqtWrXw8PBg3759KWpj165dDB48GDc3N3LkyEGPHj34+eeftXWGDx9OQEAATZo0wcrKil9//TXJCvq0adMYOHAgixYtIm/evAQGBgLg7OxMy5YtadSoESEhITRq1Ii5c+dqr+vevTuXL1+mS5cuGBgY8OOPP1KrVi2dtn/55Rd69+5NoUKFiIuLS5IS8zWSAF2k2Ms3L/FY5MHVPVdRnFOQEJrAIx69U8MCA4NudOzYnzFjXChYUPf69/+C/VrrV2KUMTQu3BgzQzOEEEII8Y/ly5cDoFKptOfy5MnDrVu3tMdjx4796O0R36pRo8YHd3kBsLS05I8//tA59/5zX02bNqVp06bJXt+3b1/69u2bbJmhoSFz587VCdrfV6lSJS5fvvzB8q+RBOgiRfae2kvbwW2JOBsBSlDzbrDtgqWlNwMHeuLjY0n27Mm38X4eeZPCTdKvw0IIIYQQmYQE6OKjqVQqdu3aha+vL/v370+mRgNsbHrw22/f0qWLEf/y0jIhhBBCCPEB8pCo+E/h4eHMnDmTwoUL07Rp0/eC82xAf6pVu8WePTtYsMAQT0+FBOdCCCFEFjd27FguXbqU0d3IlGQFXXzQrVu3mD17NsuXLycqKuq90kLo63vTsWNXhg61onhxzb6lu3al/H5qtZrExEQMDOTLUgghhBBZl6ygCx1v01gaNGhAsWLFmDNnjm5w7mhMtlwrGTnyNk+f/sDKlZrgPDUOHTpE8+bNMTU1xdDQkHz58vHzzz/z8uXL1DUshBBCCJEJyVKl4MmTJ0ybNo3ly5cn2XsUAD1DKKOECuCevyO7vTpgaa6ftF4KjBo1ivHjx+uce/r0Kb/99huLFi1i3759uLm5pcm9hBBCCCEyAwnQs7i1a9fSrVs34uPjkyktAEUcoPkxMIUh7kOZWPf3NHuL5+rVq3WCc1tbWxwdHbl48SIJCQkEBQXRuHFjbt26hfnbtxkJIYQQQnzlJMUlC1KpVOzdu5c6derQqVOnZILzOqDYAM3zQAdNcD6t3jQmeUxMs+BcrVYzceJE7fGkSZN48uQJZ8+e5cGDB5QvXx7QrKavXr06Te4phBBCCJEZSICehURGRjJnzhxcXV1p0KABhw4deqfUFOhNtmxX8fbehWv/GVDqJCRCmcAyDKw8ME37cuPGDa5fvw5A5cqVGTJkiPbh0Hz58rFgwQJt3fdfjiCEEEII8TWTFJcs4N69e8yZM4elS5cSERHxXml+oD958nRh8GAbevQAS0t4FbmNvEPzojyg5NL9S0T6RmJhYZFmfQoKCtJ+rlq1apLy0qVLY2pqSkxMjE5dIYQQQqSvI0eOUKtWLUJDQ7G2ts7o7mRJsoL+lVKr1ezfv5+mTZtSuHBhZs6c+V5wXhPYCqzD3v4ZDx/mpnSLIyQYhgCQ2yI33776Fu5qUmJev36dpv3LmTOn9nNyrxe+du0aMTExSeoKIYQQWVXNmjUZMGBARndDfAYSoH9l3rx5w7x58yhevDj16tVj586dqNXq/5eaAN8Dl2ne/DC5c68EE3deFvCl+Lwi1FpRi+WXlgOaoPzSxUvadrNnz56m/SxRogSFCxcG4OjRo8ybNw+VSgXA69ev8fLy0tZt06ZNmt5bCCGE+Bqp1WoSEhIyuhsiDUiA/gUJCQnh7NmzXLhwgdjY2E+6NiAggEGDBpEvXz68vLy4efPmO6UOwERMTZ/Qr98ibt8uyfDZZ8nV4xYMgkSPRO6G3sXcyJwYZQwqlYrx48dz//59AGrXrp3mv+LS09Nj8ODB2mMvLy9cXFyoU6cOjo6OHD9+HAAbGxu6dOmSpvcWQgghMpuuXbty9OhRZs2ahb6+PtmzZ2f58uUoFAr27t1LuXLlMDY25vjx49y/f59mzZpha2uLubk55cuX58CBAzrtxcXFMWTIEBwcHDA2NsbFxYUlS5Yke++YmBgaN25MpUqVCAkJ+RzDzfIkB/0LcPfuXUaPHs3mzZtRKpUAWFtb06NHD0aNGoWVlVWy16nVag4dOoSvry87dux4Z6X8reqAD7a2zfDxMaBPH7C0TqDq0qqceXpGs6AO8AI4D8bPjDl7+iyFPAsRGBiobWXQoEFpPWQAevTowdWrV/H19QU0P2QEBARoy62trdm+ffsHxy+EEEKklXLlyvHixYvPfl87OzvOnz//n/VmzZrFnTt3KFGiBGPHjiUyMpJHjx4BMGTIEKZOnUrBggWxtrbmyZMnNGrUiPHjx2NiYsKKFSto2rQpt2/fxtHREYAuXbpw6tQpfH19cXNz48GDB8mms4aHh9OkSRNMTEw4ePAg2bJlS9sJEMmSAD0NvX79mitXrqBWqylRogS2trb/ec2FCxeoU6dOkhcEhYWFMW3aNPbt28eRI0fIkSOHtiwqKorVq1fj5+en3QnlH8ZAJ8CbkiVLMWgQVGgQQDHbgv8vNyC/dX4uvbhEuxLtKBxRmLG/jSVBmUAwwWzfvl2ntd9++41GjRp98lx8DIVCwcyZM6lduzazZs3iyJEjqNVqrK2t6dKlCwMHDiR//vzpcm8hhBDiXS9evODp06cZ3Y0PsrKywsjICDMzM+zs7DAzM9P295dffsHDw0NbN2fOnDov+Rs/fjxbt25l+/bt9O/fnzt37rBhwwb2799P3bp1AShYsCDve/nyJe3ataNQoUKsW7cOIyOjdB6leEsC9DTw+PFjhg8fzoYNG7Qr4Pr6+rRo0YKJEydSqFChZK9LSEigdevWmuDcGLJVzoZ7CXeyB2Xnzz//JD4+nqvWV2kwsgFjB45FEaZg97rdrF6+mtDQ0Pdaywv0A3pSv34uvH+MJcRuNfP959F1/klu9rtJ0VxFAZhcdzJzG80lp5nm4cuGJRoyZcoUnRX8evXqMXDgQOrXr5/2E/YOhUJBs2bNaNasGbGxscTExGBlZYWenmRfCSGE+Hzs7Owy7X3LlSuncxwVFcW4cePYuXMnz549IyEhgZiYGO2K+6VLl9DX16dGjRr/2m7dunUpX748GzZsQF8/bd4gLj6OBOipFBAQQNWqVXn+/LnO+cTERDZt2sThw4c5evQoxYsXT3Lt9u3befDmATQCvTJ6RBlEEZwnmL0993Lnzh0qVqlIeO1wzgWeo/G3jeE28H4WC1UBHwwNm1O752E6t73D5bhJeF5aRvDpYAAM9Aw49fiUNkDPb627Kl2mTBnWrVtHbGwsISEhWFpaZsibO01MTDAxMfnvikIIIUQa+5g0ky/V+2kngwcPZu/evUydOhVnZ2dMTU1p3bq19sWEpqamH9Vu48aN2bx5Mzdu3KBkyZJp3m/xYRKgp1KXLl20wXn27Nlp3749BgYGrF+/nlevXhEcHEyHDh24fPmy9i2cykQl225vw/uct2bRG1ChomiuonR164pKrcLBwYHyFcpzYPoBiHzvpvpAScCqKTmvbcfLC3r0jsVpcX32HvmnmoOlA73K9qJH6R7kscjzn2MxMTHB3t4+1XMihBBCiLRnZGREYmLif9Y7fvw4Xbt2pUWLFoBmh7d3ny0rWbIkKpWKo0ePalNckjNx4kTMzc2pU6cOR44cwdXVNdVjEB9HAvRU8Pf358SJE4Amd+vMmTPkypULgF9//ZUqVapw/fp1rl69qt30H6Drtq6svbpW85CmCrgFK71X0rlKZx4/fszIESNZtGhRMk9K24NeT7BoSD7zaDxbZ2fELjA0VLJs40osoyyJ1ovGLNyMejnqMan5JAoWSJpTJoQQQojMx8nJiTNnzhAYGIhardZuT/w+Z2dntmzZQtOmTVEoFIwaNUqnrpOTE56ennTv3l37kOjDhw8JCgqibdu2Om1NnTqVxMREateuzZEjRyhatGi6jlFoSKJvKuzbt0/7edCgQdrgHDQPcwwbNkxzkB+27NuiLWtfvD022WyoFF8JZgIb4NyGc7Rp04YCBQowadKk94LzysA6IJCa1ceyfWVFHh6txfj+pXjzJgh3d3d6d+pNxJQIEiYlEDE/gk0TNlG0SFFWrFiRnlMghBBCiM/kp59+Ql9fnxIlSuDs7KzNKX/fjBkzyJ49O+7u7jRt2pT69etTpkwZnTrz5s2jdevWeHl5UbRoUXr27ElUVNQH22vbti21a9fmzp07aT4ukZSsoKdCdHS09vP7u428iX/DJYNL0BewhTPRZ7RljVwa8WjAI65cvEKFCRUA8PPze691Q6A94A2Uon17PX76SZ+yZf+pkZCQQNOmTXXy5kxNTbVv4FQqlXTr1g07O7t0f9hTCCGEEOmrcOHCnDp1CpVKRUREBJaWlnTv3j1JPScnJw4dOqRzrl+/fjrHJiYmTJ8+nenTpye5vmbNmkm2bvb19dVuiyzSn6ygp0KBAgW0n7dt2wbA/ZD7+Oz2Ie/0vEy7PQ1sASVYZf9nL+9nT58xbvQ4GjZsmEyrNsA44BHgCxxm3LjVrFunG5wD7Ny5k7NnzwKQN29e9u7dS1RUFM+fP6dHjx6AZq/0sWPHptWQhRBCCCFEOpMV9FRo3bo1Pj4+REVFsXjxYozzG7NcsZw3yjeaCsHAOTC4ZsDqe6v5+++/8fX1ZcuWLck85FEeGAC0Bp4CvwNLGTHCh1GjBpOc5cuXaz8vWLCAevXqAZotmxYuXMiZM2e4du0ap0+f5vbt2xQpUiQthy+EEEIIIdKBBOipYGlpyfDhw/n5559Rq9XMvjwbigNPgMNAAKCGeo3q0ahRIy5cuKBzvUJhiFrdFk0aS0WyZ7+NsfEgrK2PUK1aZfr2PUbp0qU/eP+HDx8CoKenl2Q1Xk9PjyZNmnDt2jVtXQnQhRBCCCG+fBKgp9KIESMICwtj6tSpsBUIBY4DcZpyExMTdu3apXONgYENCQl9Uat7o6eXhxYtYOBAcHcvAryfi/5hb/cqV6lUPHr0CCcnJ53y+/fvJ6krhBBCCCG+bJKDnkqJ6kSmTJnC5cuX6duzL0WfFCW7WXbtnuexsbHaugYG5YBVJCQ8Ilu2sfj45OHuXdi0CdzdP/3e766aDxkyhISEBO3xiRMn2LJFs3NMrly5KPt+ArsQQgghhPgiyQp6KiSqEmmzsQ0FzQvyTfA3nDt3jlu3bunU0dMzQKFoTWLiDyQkVCRvXgU+PtCzJ2TPnrr79+jRg99++43o6Gg2btyIv78/TZo0ITAwkJ07d2r3PO3Tpw/Gxsapu5kQQgghhPgsJEBPIbVaTY81PfhzyZ9wHnhv61Ajo9zEx/dGpeoD5KVUKRg0CNq2BSOjtOmDra0tq1evpm3btiQkJBAQEJBkC6Q6derw888/p80NhRBCCCFEupMUlxQ4c+YMpeuXZkXXFXAUneDczKw0sJz4+EfArzRpkpdDh+DCBejcOe2C87datGjBkSNHkryq187OjnHjxvHXX3/J6rkQQgghRCYiK+gfKT4+nk2bNjFr1izt3uNv6enpY2zcipgYH6Kj3TExUeDpCQMGwOd4I26VKlXYv38/jx8/JjAwkGzZslGiRAmM0vqnASGEEEIIke7SbQV97ty5FChQABMTE8qWLcvx48fT61bp6uXLl/zyyy/kz5+fTp066QTn+qamGBmNQKUKJCbmD2xsqjBunIL/tXfnUVGdZxjAnxk2F5YqGDYBQUMi7iAoUot1QTGkGpJolCa4xSKiICYG0xhIm6OGNNZwRE2OmuJW9BQ1i9owbQSsRAUOREQaPUrAxIVCEAgoAzNf/yDcMA7rAM4gz++cOYf57p17X9551Xc+73y3pATYvfvRNOfNOTk5YerUqfD09GRzTkRE1MMKCwuxd+9efPTRR8jMzNS6+2Z3W7JkCWQyGVatWqW1LTw8HDKZDEuWLOnRGB53MpkMJ06c0HcYPTODfuTIEURFRWHnzp3w8/PDRx99hMDAQFy5cgXOzs49ccpul5OTg507dyI5ORn19fWaG20BOPlAlf0VVBgID4/GZRJDQoB+/fQSLhERET0ihYWFCA8PR1pamsb4qFGjsH37dq3LTruTk5MTjhw5gri4OFhaWgJoXDHu73//u8H3WEqlkhOIHdQjM+jbtm3D8uXLsWLFCowcORLbt2+Hk5MTdu3a1ROn6zb19fU4cuQI3njjDfj6+uLAgQNScy6Xy2Ft/QLg+jYwYzaQm4GZMwfi9Gng8mVg+XI250RERI+7K1euwM/PT6s5B4CCggLMmTMHn332WY+d39PTE87Ozvj888+lsWPHjsHJyUnj5oZCCMTHx8PNzQ39+/fHuHHj8I9//EParlKpsHz5cri6uqJ///546qmn8OGHH2qcKy0tDT4+Phg4cCB+9atfwc/PT7pJ4pIlSzB//nyN/aOiojBt2jTp+bRp0xAREYHo6GjY2Nhg1qxZABpzOHfuXJibm8PW1hYvv/wyysrKNF63Zs0aREVFYdCgQbC1tcXHH3+MmpoaLF26FBYWFhg+fDhOnz6tcf6OHDcyMhJvv/02bGxsYGdnh7i4OGl70/1knnvuOchkMun5N998g9/+9rewsLCApaUlvLy8kJ2d3c471TXdPoOuVCqRk5ODmJgYjfGAgABkZmZq7V9XV4e6ujrpeVVVFYDGZllr5rqHxcfHa614MmDAYJiarsC9e6tRXu4MkyqBhUZqRF1QY+zYxviaLT/epzW9X4/6fXtcMH+6Y+50x9zpjrnrGn3nT61WS8sRd8bKlStRUVEBAHB1dcWrr74Kc3NzHDhwAFlZWVCpVFi2bBmKi4vRv3//bo1ZCAEhBEJDQ3H48GEsX74carUa+/btw9KlS5GWlgYhBNRqNd566y0cP34ciYmJePLJJ5GRkYHf//73sLa2hr+/PxoaGuDo6Ijk5GTY2NggMzMTYWFhsLW1lVaHmz9/PlasWIFDhw5BqVTi4sWL0vGbYmmew6ZLfJqPJSUlISwsDGfPnoUQAj/88AP8/f2xYsUK/OUvf8H9+/cRExODBQsW4F//+pfG615//XWcP38eR48exapVq3D8+HHMnz8fMTEx2L59O15++WV89913GDBgAG7fvt2h4+7fvx/h4eHIzMzE+fPnsWzZMvj6+mLWrFm4cOEC7OzssHfvXsyZMwdGRkZQq9UICQnB+PHjkZiYCCMjI+Tl5UnbWqNWq1us7Y7Wu0x08wVTt27dgqOjI86dO4cpze6+s3nzZiQlJeHbb7/V2D8uLg7vvPOO1nEOHz6MAQMGdGdo7frxxx+xcuVKNDQ0wNLSHXV161DX8CIwdyMGXHwTc6cqMXduEQYPftD+wYiIiMhgOTk5wc3NrVOvuXz5MqZOnQqgsTlPT0+HhYUFgMYZ6UWLFkGhUAAAEhMTsXjx4m6NOTw8HJWVlUhISMCoUaOk78VNmjQJly9fxtq1a2FlZYX3338fI0aMwKeffgofHx/p9WvXrkVtbS327NnT4vFfe+01/O9//0NSUhIqKirg5uaGL774An5+fq3GcujQIWls48aNyM/PxxdffAEACAoKQlVVFTIyMqR9Nm/ejJycHKSkpEhjP/zwA0aPHo2srCyMGDECQUFBUKlU0gy5SqWCi4sLgoKCsHv3bgCN3xF8+umnkZqaCm9vb52OCzQuRz116lRpJn3QoEE4ePAgnnnmGWkfZ2dnvPfee1i0aFE779Avbty4gZs3b2qN19bWYvHixaisrJQuUWpJj63i0nQnzSZCCK0xoPHNjI6Olp5XVVXByckJAQEBbQbeE+7cqcHw4d/j2rUpqKqaDsjUGLh0AWqcj8Ft9gUcfPUi5DLXRxpTb1JfXw+FQoFZs2bBxMRE3+H0Osyf7pg73TF3umPuukbf+bt161an+4y8vDzp59WrV8PR0VFje0xMjNSg5+TkICwsrMtxNmdiYgJjY2MMGzYMAQEBUjM6d+5cuLq6wtjYGCYmJvj+++/x4MEDBAcHa7xeqVRiwoQJ0u+9e/du7Nu3D8XFxbh//z6USiXGjx8PS0tLWFpaIjQ0FM8//zxmzpyJmTNn4sUXX4S9vb1GLM1zaGpqqjFmbGwMHx8fjX0uX76Ms2fPYujQoVq/3927d+Hp6QljY2OMHTtW43XW1tbw9PSUxpo+GNXU1MDS0rJTx216vUwmg6Ojo1az3L9/f43n69atw9q1a5GSkoIZM2bghRdewPDhw9t8r6ytrTFmzBit8aYrRdrT7Q26jY0NjIyMcOfOHY3x0tJS2Nraau1vZmbW4jrdJiYmj+wPbGVlJWJjY7F37yf46aevAXgASIfNy6+jzDkLpkam2PFMAsxMuZ54RzzK9+5xxPzpjrnTHXOnO+aua/SVP7lcDrm8c1/Fa2h2TeugQYO0Xj948GCNfTt7/PbIZDLpERISIl1OnJiYCLlcLm1rcvLkSa0PEWZmZpDL5Th69CjWr1+PDz74AL6+vrCwsMD777+PCxcuSHH/7W9/Q2RkJP75z3/i6NGj2LRpExQKBSZPngwjIyMA0Pgdm/LTfMzc3FzjuRACzz77LN577z2t38/e3l7a19TUVON1MplMa6yJXC7v8HGbak0mk0k1IITQOO7DtfHOO+8gJCQEJ0+exOnTpxEXF4fk5GQ899xzWudqfoyW6rqjtd7tDbqpqSm8vLygUCg0AlcoFJg3b153n67L7t27h2nTpuGbb775eSQCQDXgl40yNwAC2DBiA/yH+esxSiIiItI3Dw8P6eeDBw9i6dKlGg3xgQMHWty3J8ycORNKpRIAMHv2bK04zczMUFJSAn//lvuXs2fPYsqUKQgPD5fGrl+/rrXfhAkTMGHCBGzcuBG+vr44fPgwJk+ejCFDhuDy5csa++bl5bXbgHp6eiIlJQXDhg2DsXH3taHddVwTExOoVCqtcXd3d7i7u2PdunVYtGgRPvnkkzYb9K7qkVVcoqOjsWfPHuzbtw+FhYVYt24dSkpKuv2/errD+vXrpea8X79+WLzYHp6hamDWzzt8CeyK2IWamprWD0JERESPvRkzZkgre5w5cwaLFy9GVlYWCgsL8cYbb+Cvf/0rgMZLO0JDQ3s0FiMjIxQUFKCwsFCazW5iYWGB1157DevWrUNSUhKuX7+O3NxcJCYmIikpCQAwYsQIZGdn48svv8TVq1exadMmZGVlSccoKirCxo0b8fXXX6O4uBipqam4evUqRo4cCQCYPn06srOzsX//fly7dg2xsbFaDXtLVq9ejR9//BGLFi3CxYsXcePGDaSmpmLZsmUtNsYd1V3HHTZsGP7973/jzp07qKiowP379xEREYG0tDQUFxfj3LlzyMrKkvLQU3qkQV+4cCG2b9+OP/3pTxg/fjwyMjJw6tQpuLi49MTpdFZWVoaDBw8CaCzm3NxchMaF4pLbJQCAyw8uwHmgvLwchw8f1meoREREpGdGRkbYtm2b9Dw5ORk+Pj7w8PBAfHy8tIrJm2++CTs7ux6Pp+la8Zb8+c9/xttvv40tW7Zg5MiRmD17Nj7//HO4ujZ+ly4sLAzBwcFYuHAhJk2ahPLyco3Z9AEDBuC///0vnn/+ebi7u2PlypWIiIjAH/7wBwCNs/abNm3Chg0b4O3tjerqarzyyivtxuzg4IBz585BpVJh9uzZGD16NCIjI2FlZdWlS4K667gffPABFAqFtGylkZERysvL8corr8Dd3R0LFixAYGBgiwucdCthYCorKwUAUVlZ2ePnSklJEQAEALF27VohhBDXy64L563OYsHRBSLz60xpe3BwcI/H09splUpx4sQJoVQq9R1Kr8T86Y650x1zpzvmrmv0nb+SkhKdX3vw4EFhbm4u9QhNDyMjI/HWW28JtVrdjZFqU6lUoqKiQqhUqh49z+PoUeWutfrqaJ/bY6u49AbNL1tp+kTpZOmEzSM2Y97ceaitrm1xXyIiIuq7QkJCEBQUhAMHDiAzMxMNDQ0YPXo0li1b1uIqIkSd1acb9KbryADg008/RWRkJADA3NgcZsZmOHzil8tamhp4IiIiIisrK0RERCAiIkLfodBjqEeuQe8t/Pz8pHUs09LSEBUVhdLSUjQ0NCA5ORkbNmyQ9l26dKm+wiQiIiKiPqRPz6DL5XK8++670p2hEhISkJCQALlcrnH71t/97nfw9vbWV5hERERE1If06Rl0AHjppZeQkJCgsURR8+Z8zpw5OHToUIt3QSUiIiIi6m59vkEHgDVr1uDq1at4/fXX4e3tjWHDhuGFF15AamoqTp48CXNzc32HSERERER9RJ++xKU5Nzc3xMfHo76+HqdOncLcuXN562YiIqLHlLGxMX766SdOwlG3EkKgrKwMZmZmXToOG3QiIiLqc2xtbXH37l1UVFToO5ROU6vVKC8vh7W1dZdu7tMXPYrcWVlZtXoDqY5ig05ERER9jlwuh729vb7D0El9fT3y8vIwZswY/m9/J/WW3PFjFxERERGRAWGDTkRERERkQNigExEREREZEDboREREREQGxOC+JCqEAABUVVXp5fz19fWora1FVVWVQX95wBAxd13D/OmOudMdc6c75q5rmD/dMXe603fumvrbpn63NQbXoFdXVwMAnJyc9BwJEREREVH3q66uhpWVVavbZaK9Fv4RU6vVuHXrFiwsLCCTyR75+auqquDk5ISbN292eQ3Lvoa56xrmT3fMne6YO90xd13D/OmOudOdvnMnhEB1dTUcHBzaXIfd4GbQ5XI5hg4dqu8wYGlpyaLXEXPXNcyf7pg73TF3umPuuob50x1zpzt95q6tmfMm/JIoEREREZEBYYNORERERGRA2KA/xMzMDLGxsTAzM9N3KL0Oc9c1zJ/umDvdMXe6Y+66hvnTHXOnu96SO4P7kigRERERUV/GGXQiIiIiIgPCBp2IiIiIyICwQSciIiIiMiBs0ImIiIiIDAgbdCIiIiIiA8IG/SE7d+6Eq6sr+vXrBy8vL5w9e1bfIRm8uLg4yGQyjYednZ2+wzJIGRkZePbZZ+Hg4ACZTIYTJ05obBdCIC4uDg4ODujfvz+mTZuGgoIC/QRrgNrL35IlS7RqcfLkyfoJ1oBs2bIF3t7esLCwwBNPPIH58+fj22+/1diHtde6juSPtdeyXbt2YezYsdJdG319fXH69GlpO+uude3ljjXXcVu2bIFMJkNUVJQ0Zui1xwa9mSNHjiAqKgp//OMfkZubi6lTpyIwMBAlJSX6Ds3gjRo1Crdv35Ye+fn5+g7JINXU1GDcuHHYsWNHi9vj4+Oxbds27NixA1lZWbCzs8OsWbNQXV39iCM1TO3lDwDmzJmjUYunTp16hBEapvT0dKxevRrnz5+HQqFAQ0MDAgICUFNTI+3D2mtdR/IHsPZaMnToUGzduhXZ2dnIzs7G9OnTMW/ePKkRYt21rr3cAay5jsjKysLHH3+MsWPHaowbfO0Jkvj4+IiwsDCNsaefflrExMToKaLeITY2VowbN07fYfQ6AMTx48el52q1WtjZ2YmtW7dKYw8ePBBWVlZi9+7deojQsD2cPyGECA0NFfPmzdNLPL1JaWmpACDS09OFEKy9zno4f0Kw9jpj0KBBYs+ePaw7HTTlTgjWXEdUV1eLJ598UigUCuHv7y8iIyOFEL3j7zzOoP9MqVQiJycHAQEBGuMBAQHIzMzUU1S9x7Vr1+Dg4ABXV1e89NJLuHHjhr5D6nWKiopw584djRo0MzODv78/a7AT0tLS8MQTT8Dd3R2vvvoqSktL9R2SwamsrAQADB48GABrr7Mezl8T1l7bVCoVkpOTUVNTA19fX9ZdJzycuyasubatXr0azzzzDGbOnKkx3htqz1jfARiKsrIyqFQq2Nraaozb2trizp07eoqqd5g0aRL2798Pd3d33L17F++++y6mTJmCgoICWFtb6zu8XqOpzlqqweLiYn2E1OsEBgbixRdfhIuLC4qKirBp0yZMnz4dOTk5Bn9b50dFCIHo6Gj8+te/xujRowGw9jqjpfwBrL225Ofnw9fXFw8ePIC5uTmOHz8ODw8PqRFi3bWutdwBrLn2JCcnIycnB9nZ2VrbesPfeWzQHyKTyTSeCyG0xkhTYGCg9POYMWPg6+uL4cOHIykpCdHR0XqMrHdiDepu4cKF0s+jR4/GxIkT4eLigpMnTyI4OFiPkRmOiIgIXLp0Cf/5z3+0trH22tda/lh7rXvqqaeQl5eHe/fuISUlBaGhoUhPT5e2s+5a11ruPDw8WHNtuHnzJiIjI5Gamop+/fq1up8h1x4vcfmZjY0NjIyMtGbLS0tLtT5hUdsGDhyIMWPG4Nq1a/oOpVdpWvmGNdh97O3t4eLiwlr82Zo1a/DZZ5/hzJkzGDp0qDTO2uuY1vLXEtbeL0xNTTFixAhMnDgRW7Zswbhx4/Dhhx+y7jqgtdy1hDX3i5ycHJSWlsLLywvGxsYwNjZGeno6EhISYGxsLNWXIdceG/SfmZqawsvLCwqFQmNcoVBgypQpeoqqd6qrq0NhYSHs7e31HUqv4urqCjs7O40aVCqVSE9PZw3qqLy8HDdv3uzztSiEQEREBI4dO4avvvoKrq6uGttZe21rL38tYe21TgiBuro61p0OmnLXEtbcL2bMmIH8/Hzk5eVJj4kTJyIkJAR5eXlwc3Mz/NrT05dTDVJycrIwMTERe/fuFVeuXBFRUVFi4MCB4rvvvtN3aAZt/fr1Ii0tTdy4cUOcP39eBAUFCQsLC+atBdXV1SI3N1fk5uYKAGLbtm0iNzdXFBcXCyGE2Lp1q7CyshLHjh0T+fn5YtGiRcLe3l5UVVXpOXLD0Fb+qqurxfr160VmZqYoKioSZ86cEb6+vsLR0bHP52/VqlXCyspKpKWlidu3b0uP2tpaaR/WXuvayx9rr3UbN24UGRkZoqioSFy6dEm8+eabQi6Xi9TUVCEE664tbeWONdd5zVdxEcLwa48N+kMSExOFi4uLMDU1FZ6enhrLaFHLFi5cKOzt7YWJiYlwcHAQwcHBoqCgQN9hGaQzZ84IAFqP0NBQIUTj0k+xsbHCzs5OmJmZid/85jciPz9fv0EbkLbyV1tbKwICAsSQIUOEiYmJcHZ2FqGhoaKkpETfYetdSzkDID755BNpH9Ze69rLH2uvdcuWLZP+TR0yZIiYMWOG1JwLwbprS1u5Y8113sMNuqHXnkwIIR7dfD0REREREbWF16ATERERERkQNuhERERERAaEDToRERERkQFhg05EREREZEDYoBMRERERGRA26EREREREBoQNOhERERGRAWGDTkRERERkQNigExEREREZEDboREREREQGhA06EREREZEB+T8KE15y/7jQ+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we must understand that this smoothing is predicated on the system model. We have told the filter that what we are tracking follows a constant velocity model with very low process error. When the filter *looks ahead* it sees that the future behavior closely matches a constant velocity so it is able to reject most of the noise in the signal. Suppose instead our system has a lot of process noise. For example, if we are tracking a light aircraft in gusty winds its velocity will change often, and the filter will be less able to distinguish between noise and erratic movement due to the wind. We can see this in the next graph.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=7., Q=.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This underscores the fact that these filters are not *smoothing* the data in colloquial sense of the term. The filter is making an optimal estimate based on previous measurements, future measurements, and what you tell it about the behavior of the system and the noise in the system and measurements.\n",
    "\n",
    "Let's wrap this up by looking at the velocity estimates of Kalman filter vs the RTS smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gu\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(7.,show_velocity=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The improvement in the velocity, which is an hidden variable, is even more dramatic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-Lag Smoothing\n",
    "\n",
    "The RTS smoother presented above should always be your choice of algorithm if you can run in batch mode because it incorporates all available data into each estimate. Not all problems allow you to do that, but you may still be interested in receiving smoothed values for previous estimates. The number line below illustrates this concept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.book_plots import figsize\n",
    "from kf_book.smoothing_internal import *\n",
    "\n",
    "with figsize(y=2):\n",
    "    show_fixed_lag_numberline()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At step $k$ we can estimate $x_k$ using the normal Kalman filter equations. However, we can make a better estimate for $x_{k-1}$ by using the measurement received for $x_k$. Likewise, we can make a better estimate for $x_{k-2}$ by using the measurements recevied for $x_{k-1}$ and $x_{k}$. We can extend this computation back for an arbitrary $N$ steps.\n",
    "\n",
    "Derivation for this math is beyond the scope of this book; Dan Simon's *Optimal State Estimation* [2] has  a very good exposition if you are interested. The essense of the idea is that instead of having a state vector $\\mathbf{x}$ we make an augmented state containing\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}\\mathbf{x}_k \\\\ \\mathbf{x}_{k-1} \\\\ \\vdots\\\\ \\mathbf{x}_{k-N+1}\\end{bmatrix}$$\n",
    "\n",
    "This yields a very large covariance matrix that contains the covariance between states at different steps. FilterPy's class `FixedLagSmoother` takes care of all of this computation for you, including creation of the augmented matrices. All you need to do is compose it as if you are using the `KalmanFilter` class and then call `smooth()`, which implements the predict and update steps of the algorithm. \n",
    "\n",
    "Each call of `smooth` computes the estimate for the current measurement, but it also goes back and adjusts the previous `N-1` points as well. The smoothed values are contained in the list `FixedLagSmoother.xSmooth`. If you use `FixedLagSmoother.x` you will get the most recent estimate, but it is not smoothed and is no different from a standard Kalman filter output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation fixed-lag: 2.616\n",
      "standard deviation kalman: 3.564\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.kalman import FixedLagSmoother, KalmanFilter\n",
    "import numpy.random as random\n",
    "\n",
    "fls = FixedLagSmoother(dim_x=2, dim_z=1, N=8)\n",
    "\n",
    "fls.x = np.array([0., .5])\n",
    "fls.F = np.array([[1.,1.],\n",
    "                  [0.,1.]])\n",
    "\n",
    "fls.H = np.array([[1.,0.]])\n",
    "fls.P *= 200\n",
    "fls.R *= 5.\n",
    "fls.Q *= 0.001\n",
    "\n",
    "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "kf.x = np.array([0., .5])\n",
    "kf.F = np.array([[1.,1.],\n",
    "                 [0.,1.]])\n",
    "kf.H = np.array([[1.,0.]])\n",
    "kf.P *= 200\n",
    "kf.R *= 5.\n",
    "kf.Q = Q_discrete_white_noise(dim=2, dt=1., var=0.001)\n",
    "\n",
    "N = 4 # size of lag\n",
    "\n",
    "nom =  np.array([t/2. for t in range (0, 40)])\n",
    "zs = np.array([t + random.randn()*5.1 for t in nom])\n",
    "\n",
    "for z in zs:\n",
    "    fls.smooth(z)\n",
    "    \n",
    "kf_x, _, _, _ = kf.batch_filter(zs)\n",
    "x_smooth = np.array(fls.xSmooth)[:, 0]\n",
    "\n",
    "\n",
    "fls_res = abs(x_smooth - nom)\n",
    "kf_res = abs(kf_x[:, 0] - nom)\n",
    "\n",
    "plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n",
    "plt.plot(x_smooth, label='FLS')\n",
    "plt.plot(kf_x[:, 0], label='KF', ls='--')\n",
    "plt.legend(loc=4)\n",
    "\n",
    "print(f'standard deviation fixed-lag: {np.mean(fls_res):.3f}')\n",
    "print(f'standard deviation kalman: {np.mean(kf_res):.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I have set `N=8` which means that we will incorporate 8 future measurements into our estimates. This provides us with a very smooth estimate once the filter converges, at the cost of roughly 8x the amount of computation of the standard Kalman filter. Feel free to experiment with larger and smaller values of `N`. I chose 8 somewhat at random, not due to any theoretical concerns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n",
    "\n",
    "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n",
    "\n",
    "http://arc.aiaa.org/doi/abs/10.2514/3.3166"
   ]
  }
 ],
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   "language": "python",
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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